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

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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 operator. We describe the frame of wavelets for the group of parabolic automorphisms of the tree T (O p ) of balls in O p . 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 T (O p ) and obtain a rule of transformation of the introduced pseudodifferential operators with respect to mod p-affine transformations.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Sergio Albeverio

  2. Steklov Mathematical Institute, Gubkin St. 8, 119991, Moscow, Russia

    Sergei V. Kozyrev

Authors
  1. Sergio Albeverio
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  2. Sergei V. Kozyrev
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Correspondence to Sergio Albeverio.

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The text was submitted by the authors in English.

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Albeverio, S., Kozyrev, S.V. Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function. P-Adic Num Ultrametr Anal Appl 2, 21–34 (2010). https://doi.org/10.1134/S2070046610010024

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  • DOI: https://doi.org/10.1134/S2070046610010024

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