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Some equivalent multiresolution conditions on locally compact abelian groups

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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 ℝn 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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Authors and Affiliations

  1. Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    R. A. Kamyabi-Gol

  2. Center of Excellence in Analysis on Algebraic Structures (CEAAS), P.O. Box 1159-91775, Mashhad, Iran

    R. A. Kamyabi-Gol

  3. Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad, 91775, Iran

    R. Raisi Tousi

Authors
  1. R. A. Kamyabi-Gol
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  2. R. Raisi Tousi
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Correspondence to R. A. Kamyabi-Gol.

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Kamyabi-Gol, R.A., Tousi, R.R. Some equivalent multiresolution conditions on locally compact abelian groups. Proc Math Sci 120, 317–331 (2010). https://doi.org/10.1007/s12044-010-0033-0

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  • DOI: https://doi.org/10.1007/s12044-010-0033-0

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