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Multiresolution Expansions of Distributions: Pointwise Convergence and Quasiasymptotic Behavior

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Abstract

In several variables, we prove the pointwise convergence of multiresolution expansions to the distributional point values of tempered distributions and distributions of superexponential growth. The article extends and improves earlier results by G.G. Walter and B.K. Sohn and D.H. Pahk that were shown in one variable. We also provide characterizations of the quasiasymptotic behavior of distributions at finite points and discuss connections with α-density points of measures.

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Notes

  1. This definition of the order of a distributional point value is due to Łojasiewicz [9, Sect. 8]. It is more general than those used in [5, 26, 32, 37], which are rather based on (4.6).

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Rugjer Boshkovik bb, 1000, Skopje, Macedonia

    Sanja Kostadinova

  2. Department of Mathematics, Ghent University, Krijgslaan 281 Gebouw S22, B 9000, Gent, Belgium

    Jasson Vindas

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  1. Sanja Kostadinova
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  2. Jasson Vindas
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Correspondence to Jasson Vindas.

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Kostadinova, S., Vindas, J. Multiresolution Expansions of Distributions: Pointwise Convergence and Quasiasymptotic Behavior. Acta Appl Math 138, 115–134 (2015). https://doi.org/10.1007/s10440-014-9959-z

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  • DOI: https://doi.org/10.1007/s10440-014-9959-z

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