Multidimensional p-adic wavelets for the deformed metric

TL;DR

This paper develops a new framework for multidimensional p-adic wavelets based on deformed metrics, constructing wavelet bases as group orbits and analyzing their eigenvector properties with respect to pseudodifferential operators.

Contribution

It introduces deformations of the p-adic metric in multiple dimensions and constructs corresponding wavelet bases using group actions, extending existing p-adic wavelet theory.

Findings

Constructed wavelet bases as group orbits in deformed p-adic spaces

Demonstrated wavelets as eigenvectors of pseudodifferential operators

Extended p-adic wavelet theory to deformed metrics in multiple dimensions

Abstract

The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of balls in the p-adic space. In the present paper we consider deformations of the standard p-adic metric in many dimensions and construct some corresponding groups of transformations. We build several examples of p-adic wavelet bases. We show that the constructed wavelets are eigenvectors of some pseudodifferential operators.