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Further we have showed that this transform have some resembles with short" /> <meta property="article:author" content="https://independent.academia.edu/AparajitaDasgupta17" /> <meta name="description" content="By using a coset of closed subgroup, we define a generalization of directionally sensitive variant Fourier like transform for locally compact abelian (LCA) topological groups. Further we have showed that this transform have some resembles with short" /> <title>(PDF) Wavelet Multipliers and Operators on Locally Compact Groups</title> <link rel="canonical" href="https://www.academia.edu/108111466/Two_wavelet_multipliers_and_Landau_Pollak_Slepian_operators_on_locally_compact_abelian_groups_associated_to_right_H_translation_invariant_functions" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '836a04d38e13e94dcd4e9d2b995bb1a155f81b46'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1734029568000); window.Aedu.timeDifference = new Date().getTime() - 1734029568000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"By using a coset of closed subgroup, we define a generalization of directionally sensitive variant Fourier like transform for locally compact abelian (LCA) topological groups. Further we have showed that this transform have some resembles with short time Fourier transform (STFT). For particular choices of LCA group and its closed subgroup, this operator gives directional STFT of function with respect to some windows. That means the present theory extends the theory of directional STFT in LCA groups. We study the interesting properties of two wavelet multipliers on locally compact abelian topological groups associated to this transform, known as generalized two wavelet multipliers, and show that these operators are Lp-bounded for 1 ≤ p ≤ ∞, and are in Schatten-von Neumann classes, Sp. For S1 class we obtain their traces, and finally determine the connection between generalized two wavelet multipliers and generalized Landau-Pollak-Slepian operators. Mathematics Subject Classification ...","author":[{"@context":"https://schema.org","@type":"Person","name":"Aparajita Dasgupta"}],"contributor":[],"dateCreated":"2023-10-13","headline":"Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-H-translation invariant functions","image":"https://attachments.academia-assets.com/106582962/thumbnails/1.jpg","inLanguage":"en","keywords":["Mathematics","Pure Mathematics","Fourier transform"],"publisher":{"@context":"https://schema.org","@type":"Organization","name":"Research Square Platform LLC"},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}],"thumbnailUrl":"https://attachments.academia-assets.com/106582962/thumbnails/1.jpg","url":"https://www.academia.edu/108111466/Two_wavelet_multipliers_and_Landau_Pollak_Slepian_operators_on_locally_compact_abelian_groups_associated_to_right_H_translation_invariant_functions"}</script><link 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{"work":{"id":108111466,"created_at":"2023-10-13T21:49:30.812-07:00","from_world_paper_id":241929674,"updated_at":"2024-11-27T22:26:52.341-08:00","_data":{"abstract":"By using a coset of closed subgroup, we define a generalization of directionally sensitive variant Fourier like transform for locally compact abelian (LCA) topological groups. Further we have showed that this transform have some resembles with short time Fourier transform (STFT). For particular choices of LCA group and its closed subgroup, this operator gives directional STFT of function with respect to some windows. That means the present theory extends the theory of directional STFT in LCA groups. We study the interesting properties of two wavelet multipliers on locally compact abelian topological groups associated to this transform, known as generalized two wavelet multipliers, and show that these operators are Lp-bounded for 1 ≤ p ≤ ∞, and are in Schatten-von Neumann classes, Sp. For S1 class we obtain their traces, and finally determine the connection between generalized two wavelet multipliers and generalized Landau-Pollak-Slepian operators. Mathematics Subject Classification ...","publisher":"Research Square Platform LLC","ai_title_tag":"Wavelet Multipliers and Operators on Locally Compact Groups"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-H-translation invariant functions","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [279272619]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":106582962,"attachmentType":"pdf"}"><img alt="First page of “Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-H-translation invariant functions”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/106582962/mini_magick20231014-1-cdrz3u.png?1697259098" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Two wavelet multipliers and Landau-Pollak-Slepian operators on locally compact abelian groups associated to right-H-translation invariant functions</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="279272619" href="https://independent.academia.edu/AparajitaDasgupta17"><img alt="Profile image of Aparajita Dasgupta" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/279272619/127849415/117237157/s65_aparajita.dasgupta.png" />Aparajita Dasgupta</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">23 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 108111466; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">By using a coset of closed subgroup, we define a generalization of directionally sensitive variant Fourier like transform for locally compact abelian (LCA) topological groups. Further we have showed that this transform have some resembles with short time Fourier transform (STFT). For particular choices of LCA group and its closed subgroup, this operator gives directional STFT of function with respect to some windows. That means the present theory extends the theory of directional STFT in LCA groups. We study the interesting properties of two wavelet multipliers on locally compact abelian topological groups associated to this transform, known as generalized two wavelet multipliers, and show that these operators are Lp-bounded for 1 ≤ p ≤ ∞, and are in Schatten-von Neumann classes, Sp. For S1 class we obtain their traces, and finally determine the connection between generalized two wavelet multipliers and generalized Landau-Pollak-Slepian operators. Mathematics Subject Classification ...</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":106582962,"attachmentType":"pdf","workUrl":"https://www.academia.edu/108111466/Two_wavelet_multipliers_and_Landau_Pollak_Slepian_operators_on_locally_compact_abelian_groups_associated_to_right_H_translation_invariant_functions"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":106582962,"attachmentType":"pdf","workUrl":"https://www.academia.edu/108111466/Two_wavelet_multipliers_and_Landau_Pollak_Slepian_operators_on_locally_compact_abelian_groups_associated_to_right_H_translation_invariant_functions"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="106582962" data-landing_url="https://www.academia.edu/108111466/Two_wavelet_multipliers_and_Landau_Pollak_Slepian_operators_on_locally_compact_abelian_groups_associated_to_right_H_translation_invariant_functions" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="22719605" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/22719605/Orthogonal_wavelets_on_locally_compact_Abelian_groups">Orthogonal wavelets on locally compact Abelian groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7702031" href="https://independent.academia.edu/YuriFarkov">Yuri Farkov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Functional Analysis and Its Applications, 1997</p><p class="ds-related-work--abstract ds2-5-body-sm">We extend and improve the results of W. 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D. Student)</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2021</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L(G) and, using the scaling function, we construct an orthonormal wavelet basis for L(G). 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D. Student)</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Advances in Mathematics: Scientific Journal</p><p class="ds-related-work--abstract ds2-5-body-sm">We construct a wavelet frame system on locally compact abelian (LCA) group G associated with the multiresolution analysis and Haar measures. We show the characterization of the wavelet frame set and the scaling sequence on L 2 (G). The dilation and translation of wavelet frame sets for time-frequency localization in LCA groups have been set up. We obtain an orthonormal wavelet basis for L 2 (G) using the scaling sequence. We also establish the relationship between multiresolution analysis and wavelet functions. Finally, we obtain periodization for the multiresolution analysis using time-frequency localization on a periodic wavelet frame. The periodization holds wavelets' regular properties and decay conditions.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Wavelet Frames and Time-Frequency Localization in Locally Compact Abelian Groups","attachmentId":90175206,"attachmentType":"pdf","work_url":"https://www.academia.edu/85492237/Wavelet_Frames_and_Time_Frequency_Localization_in_Locally_Compact_Abelian_Groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/85492237/Wavelet_Frames_and_Time_Frequency_Localization_in_Locally_Compact_Abelian_Groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="86094949" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86094949/Fourier_Stieltjes_transform_defined_by_induced_representation_on_locally_compact_groups">Fourier-Stieltjes transform defined by induced representation on locally compact groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="137244740" href="https://independent.academia.edu/Hounkonnou">Norbert Hounkonnou</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2022</p><p class="ds-related-work--abstract ds2-5-body-sm">Abstract. In this work we extend the Fourier-Stieltjes transform of a vector measure and a continuous function defined on compact groups to locally compact groups. To do so, we consider a representation L of a normal compact subgroup K of a locally compact group G, and we use a representation of G induced by that of L. Then, we define the Fourier-Stieltjes transform of a vector measure and that of a continuous function with compact support defined on G from the representation of G. Then, we extend the Shur orthogonality relation established for compact groups to locally compact groups by using the representations of G induced by the unitary representations of one of its normal compact subgroups. This extension enables us to develop a Fourier-Stieltjes transform in series form that is linear, continuous, and invertible.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fourier-Stieltjes transform defined by induced representation on locally compact groups","attachmentId":90624887,"attachmentType":"pdf","work_url":"https://www.academia.edu/86094949/Fourier_Stieltjes_transform_defined_by_induced_representation_on_locally_compact_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/86094949/Fourier_Stieltjes_transform_defined_by_induced_representation_on_locally_compact_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="49544872" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms">Multipliers on spaces of functions on compact groups with p-summable Fourier transforms</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="152333134" href="https://independent.academia.edu/sanjivgupta21">sanjiv gupta</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Bulletin of the Australian Mathematical Society, 1993</p><p class="ds-related-work--abstract ds2-5-body-sm">Let G be a compact abelian group with dual group Γ. For 1 ≤ p &lt; ∞, denote by Ap(G) the space of integrable functions on G whose Fourier transforms belong to lp(Γ). We investigate several problems related to multipliers from Ap(G) to Aq(G). In particular, we prove that (Ap, Ap) ⊊ (Aq, Aq). For the circle group, we characterise permutation invariant multipliers from Ap to Ar for 1 ≤ r ≤ 2.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multipliers on spaces of functions on compact groups with p-summable Fourier transforms","attachmentId":67873285,"attachmentType":"pdf","work_url":"https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/49544872/Multipliers_on_spaces_of_functions_on_compact_groups_with_p_summable_Fourier_transforms"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="60108481" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/60108481/Wavelet_Transforms_for_Semidirect_Product_Groups_with_Not_Necessarily_Commutative_Normal_Subgroups">Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67770495" href="https://independent.academia.edu/HideyukiIshi">Hideyuki Ishi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Fourier Analysis and Applications, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">Let G be the semidirect product group of a separable locally compact unimodular group N of type I with a closed subgroup H of Aut(N). The group N is not necessarily commutative. We consider irreducible subrepresentations of the unitary representation of G realized naturally on L 2 (N), and investigate the wavelet transforms associated to them. Furthermore, the irreducible subspaces are characterized by certain singular integrals on N analogous to the Cauchy-Szegö integral.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Wavelet Transforms for Semidirect Product Groups with Not Necessarily Commutative Normal Subgroups","attachmentId":73695038,"attachmentType":"pdf","work_url":"https://www.academia.edu/60108481/Wavelet_Transforms_for_Semidirect_Product_Groups_with_Not_Necessarily_Commutative_Normal_Subgroups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/60108481/Wavelet_Transforms_for_Semidirect_Product_Groups_with_Not_Necessarily_Commutative_Normal_Subgroups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="86207549" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups">On the uniform convergence of Fourier transforms on groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="24490894" href="https://independent.academia.edu/ConstantineGeorgakis">Constantine Georgakis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1970</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the uniform convergence of Fourier transforms on groups","attachmentId":90714653,"attachmentType":"pdf","work_url":"https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="23879659" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/23879659/Continuous_Wavelet_Transforms_from_Semidirect_Products_Cyclic_Representations_and_Plancherel_Measure">Continuous Wavelet Transforms from Semidirect Products: Cyclic Representations and Plancherel Measure</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46150045" href="https://independent.academia.edu/HartmutF%C3%BChr">Hartmut Führ</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Fourier Analysis and Applications, 2002</p><p class="ds-related-work--abstract ds2-5-body-sm">Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R k ⋊ H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H, for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable representations, yet it is possible (and quite simple) to give admissibility conditions for a large class of them. We put these results in a theoretical context by establishing a connection to the Plancherel theory of the semidirect products, and show how the admissibility conditions relate to abstract admissibility conditions which use Plancherel theory. *</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Continuous Wavelet Transforms from Semidirect Products: Cyclic Representations and Plancherel Measure","attachmentId":44269533,"attachmentType":"pdf","work_url":"https://www.academia.edu/23879659/Continuous_Wavelet_Transforms_from_Semidirect_Products_Cyclic_Representations_and_Plancherel_Measure","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/23879659/Continuous_Wavelet_Transforms_from_Semidirect_Products_Cyclic_Representations_and_Plancherel_Measure"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":106582962,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":106582962,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_106582962" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="92379980" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/92379980/Fourier_Transform_on_Group_Like_Structures_and_Applications">Fourier Transform on Group-Like Structures and Applications</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2240411" href="https://liau.academia.edu/hassanmyrnouri">hassan myrnouri</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fourier Transforms - Approach to Scientific Principles, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fourier Transform on Group-Like Structures and Applications","attachmentId":95403865,"attachmentType":"pdf","work_url":"https://www.academia.edu/92379980/Fourier_Transform_on_Group_Like_Structures_and_Applications","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/92379980/Fourier_Transform_on_Group_Like_Structures_and_Applications"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="109451115" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/109451115/Fundamental_Theorems_of_Fourier_Stieltjes_Transform_Defined_by_Induced_Representation_on_Locally_Compact_Group">Fundamental Theorems of Fourier-Stieltjes Transform Defined by Induced Representation on Locally Compact Group</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="137244740" href="https://independent.academia.edu/Hounkonnou">Norbert Hounkonnou</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fundamental Theorems of Fourier-Stieltjes Transform Defined by Induced Representation on Locally Compact Group","attachmentId":107572730,"attachmentType":"pdf","work_url":"https://www.academia.edu/109451115/Fundamental_Theorems_of_Fourier_Stieltjes_Transform_Defined_by_Induced_Representation_on_Locally_Compact_Group","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/109451115/Fundamental_Theorems_of_Fourier_Stieltjes_Transform_Defined_by_Induced_Representation_on_Locally_Compact_Group"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="69938733" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/69938733/Multiresolution_analysis_and_Harr_like_wavelet_bases_on_locally_compact_groups">Multiresolution analysis and Harr-like wavelet bases on locally compact groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="153317761" href="https://independent.academia.edu/QingdeYang">Qingde Yang</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multiresolution analysis and Harr-like wavelet bases on locally compact groups","attachmentId":79845665,"attachmentType":"pdf","work_url":"https://www.academia.edu/69938733/Multiresolution_analysis_and_Harr_like_wavelet_bases_on_locally_compact_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/69938733/Multiresolution_analysis_and_Harr_like_wavelet_bases_on_locally_compact_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="58405037" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/58405037/Functions_that_operate_in_the_Fourier_algebra_of_a_compact_group">Functions that operate in the Fourier algebra of a compact group</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39545224" href="https://independent.academia.edu/CharlesDunkl">Charles Dunkl</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the American Mathematical Society, 1969</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Functions that operate in the Fourier algebra of a compact group","attachmentId":72838146,"attachmentType":"pdf","work_url":"https://www.academia.edu/58405037/Functions_that_operate_in_the_Fourier_algebra_of_a_compact_group","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/58405037/Functions_that_operate_in_the_Fourier_algebra_of_a_compact_group"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="54535373" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups">On the vector Fourier multipliers for compact groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Open Journal of Mathematical Sciences</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the vector Fourier multipliers for compact groups","attachmentId":70854259,"attachmentType":"pdf","work_url":"https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="122570788" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/122570788/Convolution_Operators_Supported_by_SUBGROUPS1">Convolution Operators Supported by SUBGROUPS1</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39545224" href="https://independent.academia.edu/CharlesDunkl">Charles Dunkl</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1972</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" 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Govaerts</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Mathematics and Mathematical Sciences, 1982</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The convolution-induced topology on L∞(G) and linearly dependent translates in L1(G)","attachmentId":70886805,"attachmentType":"pdf","work_url":"https://www.academia.edu/54598290/The_convolution_induced_topology_on_L_G_and_linearly_dependent_translates_in_L1_G_","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54598290/The_convolution_induced_topology_on_L_G_and_linearly_dependent_translates_in_L1_G_"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="54535359" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54535359/On_Spaces_of_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups">On Spaces of Fourier-Stieltjes Transform of Vector Measures on Compact Groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Spaces of Fourier-Stieltjes Transform of Vector Measures on Compact Groups","attachmentId":70854269,"attachmentType":"pdf","work_url":"https://www.academia.edu/54535359/On_Spaces_of_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/54535359/On_Spaces_of_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="17" data-entity-id="21796237" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/21796237/A_characterization_of_the_higher_dimensional_groups_associated_with_continuous_wavelets">A characterization of the higher dimensional groups associated with continuous wavelets</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="43012828" href="https://independent.academia.edu/LaugesenR">R. 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