Multidimensional p-adic wavelets for the deformed metric
Functional Analysis
2011-05-10 v1
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.
Cite
@article{arxiv.1105.1524,
title = {Multidimensional p-adic wavelets for the deformed metric},
author = {S. Albeverio and S. V. Kozyrev},
journal= {arXiv preprint arXiv:1105.1524},
year = {2011}
}