Some equivalent multiresolution conditions on locally compact abelian groups |
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| Authors: | R. A. Kamyabi-Gol R. Raisi Tousi |
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| Affiliation: | 1.Department of Pure Mathematics,Ferdowsi University of Mashhad,Mashhad,Iran;2.Center of Excellence in Analysis on Algebraic Structures (CEAAS),Mashhad,Iran;3.Department of Mathematics,Ferdowsi University,Mashhad,Iran |
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| Abstract: | Conditions under which a function generates a multiresolution analysis are investigated. The definition of the spectral function of a shift invariant space is generalized from ℝ n to a locally compact abelian group and the union density and intersection triviality properties of a multiresolution analysis are characterized in terms of the spectral functions. Finally, all multiresolution analysis conditions are characterized in terms of the scaling and the spectral functions. |
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