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"https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F54535371%2FFacts_About_the_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F54535371%2FFacts_About_the_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":70854282,"identifier":"Attachment_70854282","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":54535371,"created_at":"2021-10-01T02:48:30.217-07:00","from_world_paper_id":175282950,"updated_at":"2021-10-01T03:11:50.309-07:00","_data":{"abstract":"This paper gives an interpretation of the Fourier-Stieltjes trans-form of vector measures by means of the tensor product of Hilbert spaces. It also extends the Kronecker product to some operators arising from the Fourier-Stieltjes transformation and associated with the equivalence classes of unitary representations of a compact group. 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It also extends the Kronecker product to some operators arising from the Fourier-Stieltjes transformation and associated with the equivalence classes of unitary representations of a compact group. We obtain among other results the effect of this product on convolution of vector measures.</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":70854282,"attachmentType":"pdf","workUrl":"https://www.academia.edu/54535371/Facts_About_the_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups"}">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":70854282,"attachmentType":"pdf","workUrl":"https://www.academia.edu/54535371/Facts_About_the_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups"}"><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="70854282" data-landing_url="https://www.academia.edu/54535371/Facts_About_the_Fourier_Stieltjes_Transform_of_Vector_Measures_on_Compact_Groups" 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="54535359" 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/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-wsj-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--abstract ds2-5-body-sm">In [1], the author extended to vector measures on a compact non commutative group the notion of Fourier-Stieltjes transform. This brings to light some functional spaces. In this paper, we study some of their topological properties. In particular, we found their dual spaces.</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 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-wsj-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-wsj-grid-card" data-collection-position="1" data-entity-id="109451115" 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/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-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">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-wsj-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-wsj-grid-card" data-collection-position="2" 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="3" data-entity-id="70058370" 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/70058370/On_a_transform_of_Fourier_Stieltjes_type_for_C_algebra_valued_measures">On a transform of Fourier-Stieltjes type for C*-algebra valued measures</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="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Pure Mathematical Sciences, 2017</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 a transform of Fourier-Stieltjes type for C*-algebra valued measures","attachmentId":79933446,"attachmentType":"pdf","work_url":"https://www.academia.edu/70058370/On_a_transform_of_Fourier_Stieltjes_type_for_C_algebra_valued_measures","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/70058370/On_a_transform_of_Fourier_Stieltjes_type_for_C_algebra_valued_measures"><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="4" data-entity-id="86065401" 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/86065401/Fourier_Analysis_for_vector_measures">Fourier Analysis for vector-measures</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="34984782" href="https://uv.academia.edu/OscarBlasco">Oscar Blasco</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2014</p><p class="ds-related-work--abstract ds2-5-body-sm">We analyze the Fourier transform of vector measures ν as well as the convolution between scalar and vector-valued regular measures defined on the Borel sets of a compact abelian group. We make special emphasis on the Riemann-Lebesgue lemma and Young’s convolution type results in this setting. Applications to Fourier transform and convolutions between functions in Lp(ν) and, particularly, for translation invariant type measures ν are given. AMS Subj. Class: 46G10; 42A38; 46E40</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 Analysis for vector-measures","attachmentId":90601987,"attachmentType":"pdf","work_url":"https://www.academia.edu/86065401/Fourier_Analysis_for_vector_measures","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/86065401/Fourier_Analysis_for_vector_measures"><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="86740233" 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/86740233/Convolution_operators_associated_with_vector_measures">Convolution operators associated with vector measures</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="65814089" href="https://independent.academia.edu/MaRobdera">Ma Robdera</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Glasgow Mathematical Journal, 1998</p><p class="ds-related-work--abstract ds2-5-body-sm">Inthis note, we present a thorough investigation of convolution operators that are naturally associated to vector measures. We characterize those convolution operators that are weakly compact and compact on Ll(G) and C(G) as well as those that are p summing, (1 ≤ p ≤ ∞) and nuclear on C(G).</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":"Convolution operators associated with vector measures","attachmentId":91125032,"attachmentType":"pdf","work_url":"https://www.academia.edu/86740233/Convolution_operators_associated_with_vector_measures","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/86740233/Convolution_operators_associated_with_vector_measures"><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="86740326" 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/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators">Vector Measures of Bounded Semivariation and Associated Convolution Operators</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="65814089" href="https://independent.academia.edu/MaRobdera">Ma Robdera</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Glasgow Mathematical Journal, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">Let G be a compact metrizable abelian group, and let X be a Banach space. We characterize convolution operators associated with a regular Borel X-valued measure of bounded semivariation that are compact (resp; weakly compact) from L1(G), the space of integrable functions on G into L1(G) X, the injective tensor product of L1(G) and X. Along the way we prove a Fourier Convergence theorem for vector measures of relatively compact range that are absolutely continuous with respect to the Haar measure.</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":"Vector Measures of Bounded Semivariation and Associated Convolution Operators","attachmentId":91125113,"attachmentType":"pdf","work_url":"https://www.academia.edu/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators","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/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators"><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="54535372" 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/54535372/Aspects_of_the_Fourier_Stieltjes_Transform_of_C_algebra_Valued_Measures">Aspects of the Fourier-Stieltjes Transform of C*-algebra Valued Measures</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="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Advances in Mathematics and Computer Science</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper deals with the Fourier-Stieltjes transform of C∗-algebra valued measures. We construct an involution on the space of such measures, define their Fourier-Stieltjes transform and derive a convolution theorem.</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":"Aspects of the Fourier-Stieltjes Transform of C*-algebra Valued Measures","attachmentId":70854150,"attachmentType":"pdf","work_url":"https://www.academia.edu/54535372/Aspects_of_the_Fourier_Stieltjes_Transform_of_C_algebra_Valued_Measures","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/54535372/Aspects_of_the_Fourier_Stieltjes_Transform_of_C_algebra_Valued_Measures"><span class="ds2-5-text-link__content">View 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Youmbi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2015</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":"Invariant Measures on Hypergroups: An overview","attachmentId":87661160,"attachmentType":"pdf","work_url":"https://www.academia.edu/81711131/Invariant_Measures_on_Hypergroups_An_overview","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/81711131/Invariant_Measures_on_Hypergroups_An_overview"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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