Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function

Details Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function

2011-05-08

arxiv.org/abs/1105.1506v1

p-Adic Numbers, Ultrametric Analysis and Applications. 2010. V.2. No.1. P. 21-34

Mathematics

Metric Geometry

Scientific paper

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.

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