Theoretical and Mathematical Physics

, Volume 138, Issue 3, pp 322–332 | Cite as

p-Adic Pseudodifferential Operators and p-Adic Wavelets

  • S. V. Kozyrev
Article

Abstract

We introduce a new wide class of p-adic pseudodifferential operators. We show that the basis of p-adic wavelets is the basis of eigenvectors for the introduced operators.

p-adic diffusion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994); English transl., World Scientific, Singapore (1994).Google Scholar
  2. 2.
    S. V. Kozyrev, Izv. Math., 66, 367 (2002); math-ph/0012019 (2000).Google Scholar
  3. 3.
    S. Albeverio and W. Karwowosky, “A random walk on p–adic numbers,” in: Stochastic Process: Physics and Geometry II (S. Albeverio, U. Cattaneo, and D. Merlini, eds.), World Scientific, Singapore (1995), p. 61.Google Scholar
  4. 4.
    A. N. Kochubei, Theor. Math. Phys., 96, 854 (1993).Google Scholar
  5. 5.
    A. N. Kochubei, Math. USSR Izv., 39, 1263 (1992).Google Scholar
  6. 6.
    A. N. Kochubei, Pseudodifferential Equations and Stochastics over Non-Archimedean Fields, Marcel Dekker, New York (2001).Google Scholar
  7. 7.
    V. A. Avetisov, A. H. Bikulov, and S. V. Kozyrev, J. Phys. A, 32, 8785 (1999); cond-mat/9904360 (1999).Google Scholar
  8. 8.
    V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, J. Phys. A, 35, 177 (2002); cond-mat/0106506 (2001).Google Scholar
  9. 9.
    V. A. Avetisov, A. Kh. Bikulov, and V. A. Osipov, “p-Adic description of characteristic relaxation in complex systems,” J. Phys. A (submitted); cond-mat/0210447 (2002).Google Scholar
  10. 10.
    I. V. Volovich, Class. Q. Grav., 4, 83 (1987).Google Scholar
  11. 11.
    A. Khrennikov, p–Adic Valued Distributions in Mathematical Physics, Kluwer, Dordrecht (1994).Google Scholar
  12. 12.
    A. Khrennikov, Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems, and Biological Models, Kluwer, Dordrecht (1997).Google Scholar
  13. 13.
    G. S. Djordjevic and B. Dragovich, Modern Phys. Lett. A, 12, 1455 (1997).Google Scholar
  14. 14.
    G. Parisi and N. Sourlas, Eur. J. Phys. B, 14, 535 (2000); cond-mat/9906095 (1999).Google Scholar
  15. 15.
    D. M. Carlucci and C. De Dominicis, “On the replica Fourier transform,” cond-mat/9709200 (1997).Google Scholar
  16. 16.
    C. De Dominicis, D. M. Carlucci, and T. Temesvari, J. Phys. I France, 7, 105 (1997); cond-mat/9703132(1997).Google Scholar
  17. 17.
    M. Mezard, G. Parisi, and M. Virasoro, Spin-Glass Theory and Beyond, World Scientific, Singapore (1987).Google Scholar
  18. 18.
    H. Frauenfelder, Nature Struct. Biol., 2, 821 (1995).Google Scholar
  19. 19.
    D. T. Leeson and D. A. Wiersma, Nature Struct. Biol., 2, 848 (1995).Google Scholar
  20. 20.
    D. Sherrington, Phys. D, 107, 117 (1997).Google Scholar
  21. 21.
    H. Frauenfelder and D. T. Leeson, Nature Struct. Biol., 5, 757 (1998).Google Scholar
  22. 22.
    O. M. Becker and M. Karplus, J. Chem. Phys., 106, 1495 (1997).Google Scholar
  23. 23.
    J. P. Serre, Trees, Springer, New York (1980).Google Scholar
  24. 24.
    A. T. Ogielski and D. L. Stein, Phys. Rev. Lett., 55, 1634 (1985).Google Scholar
  25. 25.
    Hajime Yoshino, “Hierarchical diffusion, aging, and multifractality,” cond-mat/9604033 (1996).Google Scholar
  26. 26.
    M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Phys. Rev. Lett., 52, 1156 (1984).Google Scholar
  27. 27.
    K. Binder and A. P. Young, Rev. Modern Phys., 58, 801 (1986).Google Scholar
  28. 28.
    A. Ansary, J. Berendzen, S. F. Bowne, H. Frauenfelder, I. E. T. Iben, T. B. Sauke, E. Shyamsunder, and R. D. Young, Proc. Nat. Acad. Sci. USA, 82, 5000 (1985).Google Scholar
  29. 29.
    H. Frauenfelder, S. G. Sligar, and P. G. Wolynes, Science, 254, 1598 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • S. V. Kozyrev
    • 1
  1. 1.Institute of Chemical PhysicsRASMoscowRussia

Personalised recommendations