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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
English version PDF (230 kB) Citations (56)
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DOI: https://doi.org/10.1070/IM2005v069n05ABEH002284
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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    • This publication is cited in the following 56 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:93
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