Shannon's Sampling Theorem for Set-Valued Functions with an Application

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dc.contributor.authorYilmaz, Yilmaz
dc.contributor.authorErdogan, Bagdagul Kartal
dc.contributor.authorLevent, Halise
dc.date.accessioned2026-04-04T13:31:00Z
dc.date.available2026-04-04T13:31:00Z
dc.date.issued2024
dc.departmentİnönü Üniversitesi
dc.description.abstractIn this study, we defined a kind of Fourier expansion of set-valued square-integrable functions. In fact, we have seen that the classical Fourier basis also constitutes a basis for the Hilbert quasilinear space L2(-pi,pi,Omega(C)) of Omega(C)-valued square-integrable functions, where Omega(C) is the class of all compact subsets of complex numbers. Furthermore, we defined the quasi-Paley-Wiener space, QPW, using the Fourier transform defined for set-valued functions and thus we showed that the sequence sinc.-kk is an element of Z form also a basis for QPW. We call this result Shannon's sampling theorem for set-valued functions. Finally, we gave an application based on this theorem.
dc.identifier.doi10.3390/math12192982
dc.identifier.issn2227-7390
dc.identifier.issue19
dc.identifier.orcid0000-0003-1484-782X
dc.identifier.scopus2-s2.0-85206305222
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math12192982
dc.identifier.urihttps://hdl.handle.net/11616/108523
dc.identifier.volume12
dc.identifier.wosWOS:001331848800001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250329
dc.subjectinner-product quasilinear spaces
dc.subjectnon-deterministic signals
dc.subjectFourier expansion of set-valued square-integrable functions
dc.subjectShannon's sampling theorem for set-valued functions
dc.subjectHilbert quasilinear spaces
dc.titleShannon's Sampling Theorem for Set-Valued Functions with an Application
dc.typeArticle

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