RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2007, Volume 198, Number 1, Pages 103–126 (Mi msb1432)  

This article is cited in 23 scientific papers (total in 23 papers)

Wavelets and spectral analysis of ultrametric pseudodifferential operators

S. V. Kozyrev

Steklov Mathematical Institute, Russian Academy of Sciences

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.

DOI: https://doi.org/10.4213/sm1432

Full text: PDF file (583 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:1, 97–116

Bibliographic databases:

UDC: 517.983.37+517.984.57+517.518.34
MSC: 54E45, 42C40
Received: 24.10.2005

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
\Bibitem{Koz07}
\by S.~V.~Kozyrev
\paper Wavelets and spectral analysis
of~ultrametric pseudodifferential operators
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 1
\pages 103--126
\mathnet{http://mi.mathnet.ru/msb1432}
\crossref{https://doi.org/10.4213/sm1432}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2330687}
\zmath{https://zbmath.org/?q=an:1172.47033}
\elib{http://elibrary.ru/item.asp?id=9450881}
\transl
\jour Sb. Math.
\yr 2007
\vol 198
\issue 1
\pages 97--116
\crossref{https://doi.org/10.1070/SM2007v198n01ABEH003830}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000246564600005}
\elib{http://elibrary.ru/item.asp?id=14717678}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34249899142}


Linking options:
  • http://mi.mathnet.ru/eng/msb1432
  • https://doi.org/10.4213/sm1432
  • http://mi.mathnet.ru/eng/msb/v198/i1/p103

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Khrennikov A.Yu., Mukhamedov F.M., Mendes J.F.F., “On $p$-adic Gibbs measures of the countable state Potts model on the Cayley tree”, Nonlinearity, 20:12 (2007), 2923–2937  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. O. G. Smolyanov, N. N. Shamarov, “Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator”, Dokl. Math., 77:3 (2008), 345–349  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. O. G. Smolyanov, N. N. Shamarov, “Representation of solutions to a heat conduction equation with Vladimirov's operator by functional integrals”, Moscow University Mathematics Bulletin, 63:4 (2008), 138-143  crossref  mathscinet  mathscinet  zmath  elib  elib  scopus
    4. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    5. S. V. Kozyrev, “Toward an ultrametric theory of turbulence”, Theoret. and Math. Phys., 157:3 (2008), 1713–1722  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Dragovich B., Khrennikov A.Yu., Kozyrev S.V., Volovich I.V., “On $p$-adic mathematical physics”, P-Adic Num. Ultrametr. Anal. Appl., 1:1 (2009), 1–17  crossref  mathscinet  zmath  scopus
    7. Proc. Steklov Inst. Math., 265 (2009), 13–29  mathnet  crossref  mathscinet  zmath  isi  elib
    8. Proc. Steklov Inst. Math., 265 (2009), 165–176  mathnet  crossref  mathscinet  zmath  isi  elib
    9. Proc. Steklov Inst. Math., 265 (2009), 177–198  mathnet  crossref  mathscinet  zmath  isi  elib
    10. O. G. Smolyanov, N. N. Shamarov, “Representation of solutions to evolution equations with Vladimirov operator in terms of Feynman path integrals”, Dokl. Math., 79:2 (2009), 270–274  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    11. S.V.. Kozyrev, “Dynamics on rugged landscapes of energy and ultrametric diffusion”, P-Adic Num Ultrametr Anal Appl, 2:2 (2010), 122  crossref  mathscinet  zmath
    12. Mukhamedov F., “A dynamical system approach to phase transitions for $p$-adic potts model on the cayley tree of order two”, Rep. Math. Phys., 70:3 (2012), 385–406  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Mukhamedov F., “On dynamical systems and phase transitions for $q+1$-state $p$-adic Potts model on the Cayley tree”, Math Phys Anal Geom, 2013  crossref  mathscinet  zmath  isi  elib  scopus
    14. Farrukh Mukhamedov, Hasan Ak{\i}n, “Phase transitions forp-adic Potts model on the Cayley tree of order three”, J. Stat. Mech, 2013:07 (2013), P07014  crossref  mathscinet  isi  scopus
    15. F. M. Mukhamedov, H. Akin, “The $p$-adic Potts model on the Cayley tree of order three”, Theoret. and Math. Phys., 176:3 (2013), 1267–1279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. 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
    17. Farrukh Mukhamedov, “Renormalization Method in p-Adic λ-Model on the Cayley Tree”, Int J Theor Phys, 2015  crossref  mathscinet  scopus
    18. Khrennikov A., Oleschko K., Correa Lopez Maria de Jesus, “Modeling Fluid's Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks”, Entropy, 18:7 (2016), 249  crossref  mathscinet  isi  scopus
    19. Oleschko K., Khrennikov A., de Jesus Correa Lopez M., “P-Adic Analog of Navier–Stokes Equations: Dynamics of Fluid'S Flow in Percolation Networks (From Discrete Dynamics With Hierarchic Interactions to Continuous Universal Scaling Model)”, Entropy, 19:4 (2017), 161  crossref  mathscinet  isi  scopus
    20. Dragovich B., Khrennikov A.Yu., Kozyrev S.V., Volovich I.V., Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  scopus
    21. Theory Probab. Appl., 63:1 (2018), 94–116  mathnet  crossref  crossref  isi  elib
    22. Bendikov A., “Heat Kernels For Isotropic-Like Markov Generators on Ultrametric Spaces: a Survey”, P-Adic Numbers Ultrametric Anal. Appl., 10:1 (2018), 1–11  crossref  mathscinet  isi  scopus
    23. Bendikov A., Cygan W., Woess W., “Oscillating Heat Kernels on Ultrametric Spaces”, J. Spectr. Theory, 9:1 (2019), 195–226  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:594
    Full text:132
    References:41
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019