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

  • Sergio AlbeverioEmail author
  • Sergei V. Kozyrev
Research Articles


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.

p-adic pseudodifferential operators p-adic wavelets groups of automorphisms of trees 


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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany
  2. 2.Steklov Mathematical InstituteMoscowRussia

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