p-Adic pseudodifferential operators and p-adic wavelets

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.

arXiv comment12 pages, LaTeX, some formulas corrected

References in corpus (9)

• p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
• Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
• p-Adic description of characteristic relaxation in complex systems
• P-adic numbers and replica symmetry breaking
• Wavelet analysis as a p-adic spectral analysis
• Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
• Landscape Paradigms in Physics and Biology: Introduction and Overview
• p-Adic Path Integrals for Quadratic Actions
• Hierarchical Diffusion, Aging and Multifractality

Cited by in corpus (15)

• p-Adic Mathematical Physics
• $p$-Adic Mathematical Physics: The First 30 Years
• Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals
• Quantization of the Riemann Zeta-Function and Cosmology
• Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks
• Replica symmetry breaking related to a general ultrametric space III: the case of general measure
• Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit
• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
• Non-Degenerate Ultrametric Diffusion
• $p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators
• Hearing Shapes via p-Adic Laplacians
• $p$-Adic Haar multiresolution analysis
• $p$-Adic multiresolution analyses
• p-Adic Scaling Set and Generalized Scaling Set
• Propagator for the Free Relativistic Particle on Archimedean and Nonarchimedean Spaces