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class="js-profile-total-view-text">Public Views</span></p><p class="data"><span class="js-profile-view-count"></span></p></div></span></div><div class="suggested-academics-container"><div class="suggested-academics--header"><p class="ds2-5-body-md-bold">Related Authors</p></div><ul class="suggested-user-card-list"><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://cuhk.academia.edu/MartinManchunLi"><img class="profile-avatar u-positionAbsolute" alt="Martin Man-chun Li" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/56480/83948/3346943/s200_martin_man-chun.li.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://cuhk.academia.edu/MartinManchunLi">Martin Man-chun Li</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">The Chinese University of Hong Kong</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://deu.academia.edu/celalcem"><img class="profile-avatar u-positionAbsolute" alt="Celal Cem Sarıoğlu" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/326106/136287/158280/s200_celal_cem.sar_o_lu.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://deu.academia.edu/celalcem">Celal Cem Sarıoğlu</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Dokuz Eylül University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://kingabdulaziz.academia.edu/CenapOzel"><img class="profile-avatar u-positionAbsolute" alt="Cenap Ozel" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/326130/136298/6959670/s200_cenap.ozel.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://kingabdulaziz.academia.edu/CenapOzel">Cenap Ozel</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">King Abdulaziz University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://uohyd.academia.edu/SKumaresan"><img class="profile-avatar u-positionAbsolute" border="0" alt="" src="//a.academia-assets.com/images/s200_no_pic.png" 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Kumaresan</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Hyderabad</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://nmt.academia.edu/IvanAvramidi"><img class="profile-avatar u-positionAbsolute" alt="Ivan G Avramidi" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/861755/308395/365186/s200_ivan.avramidi.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://nmt.academia.edu/IvanAvramidi">Ivan G Avramidi</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">New Mexico Tech</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP"><img class="profile-avatar u-positionAbsolute" alt="Dr. J. M. Ashfaque (MInstP)" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/2792810/914293/18370870/s200_dr._j._m..ashfaque_amima_minstp_.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP">Dr. J. M. Ashfaque (MInstP)</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Independent Researcher</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://harvard.academia.edu/OliverKnill"><img class="profile-avatar u-positionAbsolute" alt="Oliver Knill" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/24636766/6662359/7528121/s200_oliver.knill.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://harvard.academia.edu/OliverKnill">Oliver Knill</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Harvard University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://maringa.academia.edu/MarceloCavalcanti"><img class="profile-avatar u-positionAbsolute" alt="Marcelo Cavalcanti" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/28210609/7976510/10615551/s200_marcelo.cavalcanti.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://maringa.academia.edu/MarceloCavalcanti">Marcelo Cavalcanti</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Universidade Estadual de Maringa</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://memphis.academia.edu/IrenaLasiecka"><img class="profile-avatar u-positionAbsolute" border="0" alt="" src="//a.academia-assets.com/images/s200_no_pic.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://memphis.academia.edu/IrenaLasiecka">Irena Lasiecka</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Memphis</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://bub.academia.edu/MedhaHuilgol"><img class="profile-avatar u-positionAbsolute" border="0" alt="" src="//a.academia-assets.com/images/s200_no_pic.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://bub.academia.edu/MedhaHuilgol">Medha Huilgol</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Bangalore University</p></div></div></ul></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="223886010" href="https://www.academia.edu/Documents/in/Differential_Geometry"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/SHEELPANDEY","location":"/SHEELPANDEY","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/SHEELPANDEY","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Differential Geometry"]}" data-trace="false" data-dom-id="Pill-react-component-a85951c1-03dc-4b88-bdf0-9e553fc10f24"></div> <div id="Pill-react-component-a85951c1-03dc-4b88-bdf0-9e553fc10f24"></div> </a></div></div></div></div><div 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banach and locally convex spaces" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/80162731/A_study_in_the_theory_of_multipliers_on_banach_and_locally_convex_spaces">A study in the theory of multipliers on banach and locally convex spaces</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162731"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa 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class="work-thumbnail" src="https://attachments.academia-assets.com/86636469/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162730/Weak_amenability_of_Segal_algebras">Weak amenability of Segal algebras</a></div><div class="wp-workCard_item"><span>Proceedings of the American Mathematical Society</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let G G be a locally compact abelian group, and let p ∈ [ 1 , ∞ ) p \in [1,\infty ) . We show tha...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G G be a locally compact abelian group, and let p ∈ [ 1 , ∞ ) p \in [1,\infty ) . We show that the Segal algebra S p ( G ) S_p(G) is always weakly amenable, but that it is amenable only if G G is discrete.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="082f46c4b2af93a32c624e97d32cd5dd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636469,"asset_id":80162730,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636469/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162730"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162730"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162730; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162729"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162729/Gabor_multipliers_for_weighted_Banach_spaces_on_locally_compact_abelian_groups"><img alt="Research paper thumbnail of Gabor multipliers for weighted Banach spaces on locally compact abelian groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636510/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162729/Gabor_multipliers_for_weighted_Banach_spaces_on_locally_compact_abelian_groups">Gabor multipliers for weighted Banach spaces on locally compact abelian groups</a></div><div class="wp-workCard_item"><span>Journal of Mathematics of Kyoto University</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We use a projective groups representation ρ of the unimodular group G ×Ĝ on L 2 (G) to define Gab...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We use a projective groups representation ρ of the unimodular group G ×Ĝ on L 2 (G) to define Gabor wavelet transform of a function f with respect to a window function g, where G is a locally compact abelian group andĜ its dual group. Using these transforms, we define a weighted Banach H 1, ρ w (G) and its antidual space H 1 ∼ , ρ w (G), w being a moderate weight function on G ×Ĝ. These spaces reduce to the well known Feichtinger algebra S 0 (G) and Banach space of Feichtinger distribution S 0 (G) respectively for w ≡ 1. We obtain an atomic decomposition of H 1, ρ w (G) and study some properties of Gabor multipliers on the spaces L 2 (G), H 1, ρ w (G) and H 1 ∼ , ρ w (G). Finally, we prove a theorem on the compactness of Gabor multiplier operators on L 2 (G) and H 1, ρ w (G), which reduces to an earlier result of Feichtinger [Fei 02, Theorem 5.15 (iv)] for w = 1 and G = R d .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d101bb13cd03c8394401f9a10b69b6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636510,"asset_id":80162729,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636510/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162729"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162729"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162729; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162721"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162721/Compact_Operators_on_Homogeneous_Banach_Spaces_of_Distributions_on_Locally_Compact_Abelian_Groups"><img alt="Research paper thumbnail of Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636554/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162721/Compact_Operators_on_Homogeneous_Banach_Spaces_of_Distributions_on_Locally_Compact_Abelian_Groups">Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups</a></div><div class="wp-workCard_item"><span>Southeast Asian Bulletin of Mathematics</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, two theorems about the compactness of almost invariant operators on homogeneous Ba...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian group are proved. Our theorems generalize the corresponding results of K. de Leeuw [3] and Tewari and Madan [18] for operators on homogeneous Banach spaces on the circle group and Segal algebras on a compact abelian groups, respectively.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="573a2d26020be995328c8ccd95c4d562" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636554,"asset_id":80162721,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636554/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162721"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162721"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162721; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162719"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group"><img alt="Research paper thumbnail of Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group" class="work-thumbnail" src="https://attachments.academia-assets.com/86636536/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group">Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Analysis and Applications</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Band-limited functions f can be recovered from their sampling values (f (x i)) by means of iterat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Band-limited functions f can be recovered from their sampling values (f (x i)) by means of iterative methods, if only the sampling density is high enough. We present an error analysis for these methods, treating the typical forms of errors, i.e., jitter error, truncation error, aliasing error, quantization error, and their combinations. The derived apply uniformly to whole families of spaces, e.g., to weighted L p-spaces over some locally compact Abelian group with growth rate up to some given order. In contrast to earlier papers we do not make use of any (relative) separation condition on the sampling sets. Furthermore we discard the assumption on polynomial growth of the weights that has been used over Euclidean spaces. Consequently, even for the case of regular sampling, i.e., sampling along lattices in G, the results are new in the given generality.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6fbd55581a816b305d01065c2dc4f702" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636536,"asset_id":80162719,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636536/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162719"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162719"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162719; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6fbd55581a816b305d01065c2dc4f702" } } $('.js-work-strip[data-work-id=80162719]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":80162719,"title":"Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group","internal_url":"https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group","owner_id":223886010,"coauthors_can_edit":true,"owner":{"id":223886010,"first_name":"SHEEL","middle_initials":null,"last_name":"PANDEY","page_name":"SHEELPANDEY","domain_name":"independent","created_at":"2022-05-17T23:50:25.745-07:00","display_name":"SHEEL PANDEY","url":"https://independent.academia.edu/SHEELPANDEY"},"attachments":[{"id":86636536,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/86636536/thumbnails/1.jpg","file_name":"82475147.pdf","download_url":"https://www.academia.edu/attachments/86636536/download_file","bulk_download_file_name":"Error_estimates_for_irregular_sampling_o.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/86636536/82475147-libre.pdf?1653810877=\u0026response-content-disposition=attachment%3B+filename%3DError_estimates_for_irregular_sampling_o.pdf\u0026Expires=1740545276\u0026Signature=bejkSXEm1Iho-Kb9GURq3y1Z23F04ngTyeBjPyIUIARnaI8y~Xabyun9ce8YBrOKqH8HhRseeW1e0pG8mwGGZYkZaq-YeD49XvJV0aIm5ZWVvGG5AEDWyYiaG3v8FYsIW~dOMdW-O2LQobQ4IOYMxHrx02srCNxr~tzA7Mwnutmb1ycaZYqg~Ay2Q11DfbkHEiyhFHMab8a9UkW5wjRobLbeu9G5RdINPJNkg-v~2QYnx93g5Qk5EQYuj62PjDeoyKFMa3jRDxpHbrranIAK9hhxBsbZNCHQMt2sh4A2jR8BZfnIOuyv3rQ---gdaeDOq07YVdt6b4TdmaFT-af8VA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162717"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162717/Compactness_in_Wiener_amalgams_on_locally_compact_groups"><img alt="Research paper thumbnail of Compactness in Wiener amalgams on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636618/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162717/Compactness_in_Wiener_amalgams_on_locally_compact_groups">Compactness in Wiener amalgams on locally compact groups</a></div><div class="wp-workCard_item"><span>International Journal of Mathematics and Mathematical Sciences</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We study the compactness of bounded subsets in a Wiener amalgam whose local and global components...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group. Our main theorem provides a generalization of the corresponding results of Feichtinger. This paper paves the way for the study of compact multiplier operators on general Wiener amalgams on the lines of Feichtinger.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="59d68f20df29ffcb55bd1645c4808ade" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636618,"asset_id":80162717,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636618/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162717"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162717"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162717; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162665"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162665/Minimal_norm_interpolation_in_harmonic_Hilbert_spaces_and_Wiener_amalgam_spaces_on_locally_compact_abelian_groups"><img alt="Research paper thumbnail of Minimal norm interpolation in harmonic Hilbert spaces and Wiener amalgam spaces on locally compact abelian groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636479/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162665/Minimal_norm_interpolation_in_harmonic_Hilbert_spaces_and_Wiener_amalgam_spaces_on_locally_compact_abelian_groups">Minimal norm interpolation in harmonic Hilbert spaces and Wiener amalgam spaces on locally compact abelian groups</a></div><div class="wp-workCard_item"><span>Journal of Mathematics of Kyoto University</span><span>, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The family of harmonic Hilbert spaces is a natural enlargement of those classical L 2-Sobolev spa...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The family of harmonic Hilbert spaces is a natural enlargement of those classical L 2-Sobolev space on R d which consist of continuous functions. In the present paper we demonstrate that the use of basic results from the theory of Wiener amalgam spaces allows to establish fundamental properties of harmonic Hilbert spaces even if they are defined over an arbitrary locally compact abelian group G. Even for G = R d this new approach improves previously known results. In this paper we present results on minimal norm interpolators over lattices and show that the infinite minimal norm interpolations are the limits of finite minimal norm interpolations. In addition, the new approach paves the way for the study of stability problems and error analysis for norm interpolations in harmonic Hilbert and Banach spaces on locally compact abelian groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0a49a39b50a1da14549b915c93d0b24f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636479,"asset_id":80162665,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636479/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162665"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162665"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162665; 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We show tha...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G G be a locally compact abelian group, and let p ∈ [ 1 , ∞ ) p \in [1,\infty ) . We show that the Segal algebra S p ( G ) S_p(G) is always weakly amenable, but that it is amenable only if G G is discrete.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="082f46c4b2af93a32c624e97d32cd5dd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636469,"asset_id":80162730,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636469/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162730"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162730"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162730; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162729"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162729/Gabor_multipliers_for_weighted_Banach_spaces_on_locally_compact_abelian_groups"><img alt="Research paper thumbnail of Gabor multipliers for weighted Banach spaces on locally compact abelian groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636510/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162729/Gabor_multipliers_for_weighted_Banach_spaces_on_locally_compact_abelian_groups">Gabor multipliers for weighted Banach spaces on locally compact abelian groups</a></div><div class="wp-workCard_item"><span>Journal of Mathematics of Kyoto University</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We use a projective groups representation ρ of the unimodular group G ×Ĝ on L 2 (G) to define Gab...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We use a projective groups representation ρ of the unimodular group G ×Ĝ on L 2 (G) to define Gabor wavelet transform of a function f with respect to a window function g, where G is a locally compact abelian group andĜ its dual group. Using these transforms, we define a weighted Banach H 1, ρ w (G) and its antidual space H 1 ∼ , ρ w (G), w being a moderate weight function on G ×Ĝ. These spaces reduce to the well known Feichtinger algebra S 0 (G) and Banach space of Feichtinger distribution S 0 (G) respectively for w ≡ 1. We obtain an atomic decomposition of H 1, ρ w (G) and study some properties of Gabor multipliers on the spaces L 2 (G), H 1, ρ w (G) and H 1 ∼ , ρ w (G). Finally, we prove a theorem on the compactness of Gabor multiplier operators on L 2 (G) and H 1, ρ w (G), which reduces to an earlier result of Feichtinger [Fei 02, Theorem 5.15 (iv)] for w = 1 and G = R d .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d101bb13cd03c8394401f9a10b69b6e8" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636510,"asset_id":80162729,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636510/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162729"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162729"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162729; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162723"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162723/A_Multiplier_Problem_for_Fourier_Jacobi_Expansions_in_a_Banach_Space"><img alt="Research paper thumbnail of A Multiplier Problem for Fourier-Jacobi Expansions in a Banach Space" class="work-thumbnail" src="https://attachments.academia-assets.com/86636503/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162723/A_Multiplier_Problem_for_Fourier_Jacobi_Expansions_in_a_Banach_Space">A Multiplier Problem for Fourier-Jacobi Expansions in a Banach Space</a></div><div class="wp-workCard_item"><span>Tokyo Journal of Mathematics</span><span>, 1992</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="68b407814e0b1579e02670c1523a1a2d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636503,"asset_id":80162723,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636503/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162723"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162723"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162723; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162721"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162721/Compact_Operators_on_Homogeneous_Banach_Spaces_of_Distributions_on_Locally_Compact_Abelian_Groups"><img alt="Research paper thumbnail of Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636554/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162721/Compact_Operators_on_Homogeneous_Banach_Spaces_of_Distributions_on_Locally_Compact_Abelian_Groups">Compact Operators on Homogeneous Banach Spaces of Distributions on Locally Compact Abelian Groups</a></div><div class="wp-workCard_item"><span>Southeast Asian Bulletin of Mathematics</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper, two theorems about the compactness of almost invariant operators on homogeneous Ba...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper, two theorems about the compactness of almost invariant operators on homogeneous Banach spaces of distributions (in the sense of Feichtinger [11]) defined on a locally compact abelian group are proved. Our theorems generalize the corresponding results of K. de Leeuw [3] and Tewari and Madan [18] for operators on homogeneous Banach spaces on the circle group and Segal algebras on a compact abelian groups, respectively.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="573a2d26020be995328c8ccd95c4d562" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636554,"asset_id":80162721,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636554/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162721"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162721"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162721; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162719"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group"><img alt="Research paper thumbnail of Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group" class="work-thumbnail" src="https://attachments.academia-assets.com/86636536/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group">Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Analysis and Applications</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Band-limited functions f can be recovered from their sampling values (f (x i)) by means of iterat...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Band-limited functions f can be recovered from their sampling values (f (x i)) by means of iterative methods, if only the sampling density is high enough. We present an error analysis for these methods, treating the typical forms of errors, i.e., jitter error, truncation error, aliasing error, quantization error, and their combinations. The derived apply uniformly to whole families of spaces, e.g., to weighted L p-spaces over some locally compact Abelian group with growth rate up to some given order. In contrast to earlier papers we do not make use of any (relative) separation condition on the sampling sets. Furthermore we discard the assumption on polynomial growth of the weights that has been used over Euclidean spaces. Consequently, even for the case of regular sampling, i.e., sampling along lattices in G, the results are new in the given generality.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6fbd55581a816b305d01065c2dc4f702" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636536,"asset_id":80162719,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636536/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162719"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162719"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162719; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6fbd55581a816b305d01065c2dc4f702" } } $('.js-work-strip[data-work-id=80162719]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":80162719,"title":"Error estimates for irregular sampling of band-limited functions on a locally compact Abelian group","internal_url":"https://www.academia.edu/80162719/Error_estimates_for_irregular_sampling_of_band_limited_functions_on_a_locally_compact_Abelian_group","owner_id":223886010,"coauthors_can_edit":true,"owner":{"id":223886010,"first_name":"SHEEL","middle_initials":null,"last_name":"PANDEY","page_name":"SHEELPANDEY","domain_name":"independent","created_at":"2022-05-17T23:50:25.745-07:00","display_name":"SHEEL PANDEY","url":"https://independent.academia.edu/SHEELPANDEY"},"attachments":[{"id":86636536,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/86636536/thumbnails/1.jpg","file_name":"82475147.pdf","download_url":"https://www.academia.edu/attachments/86636536/download_file","bulk_download_file_name":"Error_estimates_for_irregular_sampling_o.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/86636536/82475147-libre.pdf?1653810877=\u0026response-content-disposition=attachment%3B+filename%3DError_estimates_for_irregular_sampling_o.pdf\u0026Expires=1740545276\u0026Signature=bejkSXEm1Iho-Kb9GURq3y1Z23F04ngTyeBjPyIUIARnaI8y~Xabyun9ce8YBrOKqH8HhRseeW1e0pG8mwGGZYkZaq-YeD49XvJV0aIm5ZWVvGG5AEDWyYiaG3v8FYsIW~dOMdW-O2LQobQ4IOYMxHrx02srCNxr~tzA7Mwnutmb1ycaZYqg~Ay2Q11DfbkHEiyhFHMab8a9UkW5wjRobLbeu9G5RdINPJNkg-v~2QYnx93g5Qk5EQYuj62PjDeoyKFMa3jRDxpHbrranIAK9hhxBsbZNCHQMt2sh4A2jR8BZfnIOuyv3rQ---gdaeDOq07YVdt6b4TdmaFT-af8VA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162717"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162717/Compactness_in_Wiener_amalgams_on_locally_compact_groups"><img alt="Research paper thumbnail of Compactness in Wiener amalgams on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636618/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162717/Compactness_in_Wiener_amalgams_on_locally_compact_groups">Compactness in Wiener amalgams on locally compact groups</a></div><div class="wp-workCard_item"><span>International Journal of Mathematics and Mathematical Sciences</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We study the compactness of bounded subsets in a Wiener amalgam whose local and global components...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We study the compactness of bounded subsets in a Wiener amalgam whose local and global components are solid Banach function (BF) spaces on a locally compact group. Our main theorem provides a generalization of the corresponding results of Feichtinger. This paper paves the way for the study of compact multiplier operators on general Wiener amalgams on the lines of Feichtinger.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="59d68f20df29ffcb55bd1645c4808ade" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636618,"asset_id":80162717,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636618/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162717"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162717"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162717; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="80162665"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/80162665/Minimal_norm_interpolation_in_harmonic_Hilbert_spaces_and_Wiener_amalgam_spaces_on_locally_compact_abelian_groups"><img alt="Research paper thumbnail of Minimal norm interpolation in harmonic Hilbert spaces and Wiener amalgam spaces on locally compact abelian groups" class="work-thumbnail" src="https://attachments.academia-assets.com/86636479/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/80162665/Minimal_norm_interpolation_in_harmonic_Hilbert_spaces_and_Wiener_amalgam_spaces_on_locally_compact_abelian_groups">Minimal norm interpolation in harmonic Hilbert spaces and Wiener amalgam spaces on locally compact abelian groups</a></div><div class="wp-workCard_item"><span>Journal of Mathematics of Kyoto University</span><span>, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The family of harmonic Hilbert spaces is a natural enlargement of those classical L 2-Sobolev spa...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The family of harmonic Hilbert spaces is a natural enlargement of those classical L 2-Sobolev space on R d which consist of continuous functions. In the present paper we demonstrate that the use of basic results from the theory of Wiener amalgam spaces allows to establish fundamental properties of harmonic Hilbert spaces even if they are defined over an arbitrary locally compact abelian group G. Even for G = R d this new approach improves previously known results. In this paper we present results on minimal norm interpolators over lattices and show that the infinite minimal norm interpolations are the limits of finite minimal norm interpolations. In addition, the new approach paves the way for the study of stability problems and error analysis for norm interpolations in harmonic Hilbert and Banach spaces on locally compact abelian groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0a49a39b50a1da14549b915c93d0b24f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":86636479,"asset_id":80162665,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/86636479/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="80162665"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80162665"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80162665; 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