Coincidence of the continuous and discrete p-adic wavelet transforms
Abstract
Description
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.
12 pages
12 pages