Multidimensional p-adic wavelets for the deformed metric

Details Multidimensional p-adic wavelets for the deformed metric Multidimensional p-adic wavelets for the deformed metric

2011-05-08

arxiv.org/abs/1105.1524v1

p-Adic Numbers, Ultrametric Analysis and Applications, 2010. V.2. N.4. P.265-277

Mathematics

Functional Analysis

Scientific paper

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.

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