Coincidence of the continuous and discrete p-adic wavelet transforms

Details Coincidence of the continuous and discrete p-adic wavelet transforms Coincidence of the continuous and discrete p-adic wavelet transforms

2007-02-02

arxiv.org/abs/math-ph/0702010v1

Physics

Mathematical Physics

12 pages

Scientific paper

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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