TRANSLATION, MODULATION AND DILATION SYSTEMS IN SET-VALUED SIGNAL PROCESSING

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dc.authoridYilmaz, Yilmaz/0000-0003-1484-782X
dc.authorwosidYilmaz, Yilmaz/A-9582-2018
dc.contributor.authorLevent, H.
dc.contributor.authorYilmaz, Y.
dc.date.accessioned2024-08-04T21:02:17Z
dc.date.available2024-08-04T21:02:17Z
dc.date.issued2018
dc.departmentİnönü Üniversitesien_US
dc.description.abstractIn this paper, we investigate a very important function space consists of set-valued functions defined on the set of real numbers with values on the space of all compact-convex subsets of complex numbers for which the pth power of their norm is integrable. In general, this space is denoted by L-p (R, Omega(C)) for 1 <= p < infinity and it has an algebraic structure named as a quasilinear space which is a generalization of a classical linear space. Further, we introduce an inner-product (set-valued inner product) on L-2 (R, Omega(C)) and we think it is especially important to manage interval-valued data and interval-based signal processing. This also can be used in imprecise expectations. The definition of inner-product on L-2 (R, Omega(C)) is based on Aumann integral which is ready for use integration of set-valued functions and we show that the space L-2 (R, Omega(C)) is a Hilbert quasilinear space. Finally, we give translation, modulation and dilation operators which are three fundational set-valued operators on Hilbert quasilinear space L-2 (R, Omega(C)).en_US
dc.identifier.doi10.15330/cmp.10.1.143-164
dc.identifier.endpage164en_US
dc.identifier.issn2075-9827
dc.identifier.issn2313-0210
dc.identifier.issue1en_US
dc.identifier.startpage143en_US
dc.identifier.urihttps://doi.org/10.15330/cmp.10.1.143-164
dc.identifier.urihttps://hdl.handle.net/11616/104630
dc.identifier.volume10en_US
dc.identifier.wosWOS:000437802500012en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherVasyl Stefanyk Precarpathian Natl Univen_US
dc.relation.ispartofCarpathian Mathematical Publicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectHilbert quasilinear spaceen_US
dc.subjectset-valued functionen_US
dc.subjectAumann integralen_US
dc.subjecttranslationen_US
dc.subjectmodulationen_US
dc.subjectdilationen_US
dc.titleTRANSLATION, MODULATION AND DILATION SYSTEMS IN SET-VALUED SIGNAL PROCESSINGen_US
dc.typeArticleen_US

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