Multidimensional basis of p-adic wavelets and representation theory

Abstract

A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of products of the vectors from the constructed basis and p-roots of one is the orbit of the corresponding p-adic group of linear transformations.

12 pages

References in corpus (4)

• Coincidence of the continuous and discrete p-adic wavelet transforms
• $p$-Adic Haar multiresolution analysis
• Frames of p-adic wavelets and orbits of the affine group
• A wavelet theory for local fields and related groups

Cited by in corpus (3)

• Cuntz-Krieger algebras and wavelets on fractals
• Multidimensional p-adic wavelets for the deformed metric
• Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function