Coincidence of the continuous and discrete p-adic wavelet transforms

2007/02/02 by Sergio Albeverio, Albeverio, S., С. В. Козырев +1
Mathematics · #42C40 #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math-ph/0702010

openalex publication_date 2007/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform coincides with the discrete p-adic wavelet transform. The p-adic multiresolution approximation is introduced and relation with the real multiresolution approximation is described. Relation of application of p-adic wavelets to spectral theory of p-adic pseudodifferential operators and the known results about sparsity of matrices of some real integral operators in the bases of multiresolution wavelets is discussed.

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