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

Autor:	Yılmaz Yılmaz, Bağdagül Kartal Erdoğan, Halise Levent
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	inner-product quasilinear spaces non-deterministic signals Fourier expansion of set-valued square-integrable functions Shannon’s sampling theorem for set-valued functions Hilbert quasilinear spaces Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 19, p 2982 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12192982
Popis:	In 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(−π,π,Ω(C)) of Ω(C)-valued square-integrable functions, where Ω(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∈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.
Databáze:	Directory of Open Access Journals
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