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Tr. Mat. Inst. Steklova, 2009, Volume 265, Pages 19–35 (Mi tm819)  

This article is cited in 7 scientific papers (total in 7 papers)

Multidimensional Ultrametric Pseudodifferential Equations

S. Albeverioab, S. V. Kozyrevc

a Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany
b Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, Bonn, Germany
c Steklov Mathematical Institute, Moscow, Russia

Abstract: We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and the space $D'_0(X)$ of generalized functions on a multidimensional ultrametric space. We also consider some family of pseudodifferential operators on multidimensional ultrametric spaces. The notions of Cauchy problem for ultrametric pseudodifferential equations and of ultrametric characteristics are introduced. We prove an existence theorem and describe all solutions for the Cauchy problem (an analog of the Kovalevskaya theorem).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 265, 13–29

Bibliographic databases:

Document Type: Article
UDC: 517.96
Received in December 2008
Language: English

Citation: S. Albeverio, S. V. Kozyrev, “Multidimensional Ultrametric Pseudodifferential Equations”, Selected topics of mathematical physics and $p$-adic analysis, Collected papers, Tr. Mat. Inst. Steklova, 265, MAIK Nauka/Interperiodica, Moscow, 2009, 19–35; Proc. Steklov Inst. Math., 265 (2009), 13–29

Citation in format AMSBIB
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\by S.~Albeverio, S.~V.~Kozyrev
\paper Multidimensional Ultrametric Pseudodifferential Equations
\inbook Selected topics of mathematical physics and $p$-adic analysis
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2009
\vol 265
\pages 19--35
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2009
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\pages 13--29
\crossref{https://doi.org/10.1134/S0081543809020023}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 265 (2009), 143–147  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Albeverio S., Khrennikov A.Yu., Shelkovich V.M., “The Cauchy problems for evolutionary pseudo-differential equations over $p$-adic field and the wavelet theory”, J. Math. Anal. Appl., 375:1 (2011), 82–98  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Kozyrev S.V., Khrennikov A.Yu., “$p$-adic integral operators in wavelet bases”, Dokl. Math., 83:2 (2011), 209–212  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. Khrennikov A.Y., Kosyak A.V., Shelkovich V.M., “Wavelet Analysis on Adeles and Pseudo-Differential Operators”, J. Fourier Anal. Appl., 18:6 (2012), 1215–1264  crossref  mathscinet  zmath  isi  elib  scopus
    6. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
    7. Behera B., Jahan Q., “Affine, Quasi-Affine and Co-Affine Frames on Local Fields of Positive Characteristic”, Math. Nachr., 290:14-15 (2017), 2154–2169  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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