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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. 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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.","publisher":"Cambridge University Press (CUP)","publication_date":"2010,,","publication_name":"Glasgow Mathematical Journal"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Vector Measures of Bounded Semivariation and Associated Convolution Operators","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [65814089]; 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.loswp.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":91125113,"attachmentType":"pdf"}"><img alt="First page of “Vector Measures of Bounded Semivariation and Associated Convolution Operators”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/91125113/mini_magick20220916-1-1om0795.png?1663325173" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.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">Vector Measures of Bounded Semivariation and Associated Convolution Operators</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="65814089" href="https://independent.academia.edu/MaRobdera"><img alt="Profile image of Ma Robdera" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Ma Robdera</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2010, Glasgow Mathematical Journal</p><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">8 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 = 86740326; 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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-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":91125113,"attachmentType":"pdf","workUrl":"https://www.academia.edu/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators"}">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":91125113,"attachmentType":"pdf","workUrl":"https://www.academia.edu/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators"}"><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="91125113" data-landing_url="https://www.academia.edu/86740326/Vector_Measures_of_Bounded_Semivariation_and_Associated_Convolution_Operators" 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. 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