Translation, modulation and dilation systems in set-valued signal processing
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 1
Abstract
In 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 Lp for 1≤p<∞ 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 L2(R,Ω(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 L2(R,Ω(C)) is based on Aumann integral which is ready for use integration of set-valued functions and we show that the space L2(R,Ω(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 L2(R,Ω(C)).
Authors and Affiliations
H. Levent, Y. Yilmaz
Keywords
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- DOI 10.15330/cmp.10.1.143-164
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