Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function
Abstract
We discuss transformation of p-adic pseudodifferential operators (in the one-dimensional and multidimensional cases) with respect to p-adic maps which correspond to automorphisms of the tree of balls in the corresponding p-adic spaces. In the dimension one we find a rule of transformation for pseudodifferential operators. In particular we find the formula of pseudodifferentiation of a composite function with respect to the Vladimirov p-adic fractional differentiation operator. We describe the frame of wavelets for the group of parabolic automorphisms of the tree of balls in the p-adic field. In many dimensions we introduce the group of mod p-affine transformations, the family of pseudodifferential operators corresponding to pseudodifferentiation along vector fields on the tree of balls in p-adic miltidimensional space and obtain a rule of transformation of the introduced pseudodifferential operators with respect to mod p-affine transformations.
Cite
@article{arxiv.1105.1506,
title = {Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function},
author = {S. Albeverio and S. V. Kozyrev},
journal= {arXiv preprint arXiv:1105.1506},
year = {2011}
}