Abstract
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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Albeverio, S., Kozyrev, S.V. Multidimensional p-adic wavelets for the deformed metric. P-Adic Num Ultrametr Anal Appl 2, 265–277 (2010). https://doi.org/10.1134/S2070046610040011
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DOI: https://doi.org/10.1134/S2070046610040011