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Izvestiya: Mathematics, 2005, Volume 69, Issue 5, Pages 989–1003
DOI: https://doi.org/10.1070/IM2005v069n05ABEH002284
(Mi im657)
 

This article is cited in 56 scientific papers (total in 56 papers)

Pseudodifferential operators on ultrametric spaces and ultrametric wavelets

S. V. Kozyrev, A. Yu. Khrennikov
References:
Abstract: We construct a wavelet analysis and spectral theory of pseudodifferential operators on general ultrametric spaces. Operators generalizing the Vladimirov operator of $p$-adic fractional differentiation are introduced. We construct a family of ultrametric wavelet bases in spaces of square-integrable complex-valued functions for a wide family of ultrametric spaces. We show that the pseudodifferential operators introduced are diagonal in these wavelet bases and compute the corresponding eigenvalues.
Received: 08.04.2004
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2005, Volume 69, Issue 5, Pages 133–148
DOI: https://doi.org/10.4213/im657
Bibliographic databases:
Document Type: Article
UDC: 517.58
MSC: 35S05, 47G10, 26E30
Language: English
Original paper language: Russian
Citation: S. V. Kozyrev, A. Yu. Khrennikov, “Pseudodifferential operators on ultrametric spaces and ultrametric wavelets”, Izv. RAN. Ser. Mat., 69:5 (2005), 133–148; Izv. Math., 69:5 (2005), 989–1003
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/im657
  • https://doi.org/10.1070/IM2005v069n05ABEH002284
  • https://www.mathnet.ru/eng/im/v69/i5/p133
  • This publication is cited in the following 56 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:766
    Russian version PDF:256
    English version PDF:22
    References:93
    First page:2
     
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