p-Adic Pseudodifferential Operators and p-Adic Wavelets

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.

[1]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[2]  p-Adic Path Integrals for Quadratic Actions , 1997, math-ph/0005026.

[3]  M. Mézard,et al.  Nature of the Spin-Glass Phase , 1984 .

[4]  Igor Volovich,et al.  p-adic string , 1987 .

[5]  V A Avetisov,et al.  p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes , 2002 .

[6]  P. Wolynes,et al.  The energy landscapes and motions of proteins. , 1991, Science.

[7]  Ogielski,et al.  Dynamics on ultrametric spaces. , 1985, Physical review letters.

[8]  V. Avetisov,et al.  p-Adic description of characteristic relaxation in complex systems , 2002, cond-mat/0210447.

[9]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[10]  David Sherrington Landscape paradigms in physics and biology: Introduction and overview , 1996 .

[11]  Anatoly N. Kochubei,et al.  Pseudo-differential equations and stochastics over non-archimedean fields , 2001 .

[12]  Andrei Khrennikov,et al.  p-Adic Valued Distributions in Mathematical Physics , 1994 .

[13]  A. Kochubei,et al.  PARABOLIC EQUATIONS OVER THE FIELD OF $ p$-ADIC NUMBERS , 1992 .

[14]  S. V. Kozyrev,et al.  Application of p-adic analysis to models of breaking of replica symmetry , 1999 .

[15]  A. Kochubei Onp-adic Green's functions , 1993 .

[16]  Hierarchical diffusion, aging and multifractality , 1996, cond-mat/9604033.

[17]  Nellie Clarke Brown Trees , 1896, Savage Dreams.

[18]  M. Karplus,et al.  The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics , 1997 .