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Sbornik: Mathematics, 2007, Volume 198, Issue 1, Pages 97–116
DOI: https://doi.org/10.1070/SM2007v198n01ABEH003830 (Mi sm1432) 		 
This article is cited in 34 scientific papers (total in 34 papers)

Wavelets and spectral analysis of ultrametric pseudodifferential operators

S. V. Kozyrev

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (341 kB) Citations (34)
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DOI: https://doi.org/10.1070/SM2007v198n01ABEH003830
Abstract: The spectral theory of pseudodifferential operators on ultrametric spaces of general form is investigated with the use of the analysis of ultrametric wavelets. Bases of ultrametric wavelets are constructed on ultrametric spaces of analytic type; it is proved that bases of ultrametric wavelets are bases of eigenvectors for the introduced pseudodifferential operators and the corresponding eigenvalues are calculated. A generalization of the Vladimirov operator of $p$-adic fractional derivation is introduced for general ultrametric spaces.
Bibliography: 32 titles.
Received: 24.10.2005
Russian version:
Matematicheskii Sbornik, 2007, Volume 198, Number 1, Pages 103–126
DOI: https://doi.org/10.4213/sm1432
Bibliographic databases:
Document Type: Article
UDC: 517.983.37+517.984.57+517.518.34
MSC: 54E45, 42C40
Language: English
Original paper language: Russian
Citation: S. V. Kozyrev, “Wavelets and spectral analysis of ultrametric pseudodifferential operators”, Mat. Sb., 198:1 (2007), 103–126; Sb. Math., 198:1 (2007), 97–116
Citation in format AMSBIB
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    • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:74
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