Approximation of functions by n-separate wavelets in the spaces Lp(R), 1 ≤ p ≤ ∞

Abstract

We consider the orthonormal bases of n-separate MRAs and wavelets constructed by the author earlier. The classical wavelet basis of the space L2(R) is formed by shifts and compressions of a single function ψ. In contrast to the classical case, we consider a basis of L2(R) formed by shifts and compressions of n functions ψs, s = 1, . , n. The constructed n-separate wavelets form an orthonormal basis of L2(R). In this case, the series Σn s=1Σj∈ZΣk∈Zhf, ψs nj+siψs nj+s converges to the function f in the space L2(R). We write additional constraints on the functions φs and ψs, s = 1, . , n, that provide the convergence of the series to the function f in the spaces Lp(R), 1 ≤ p ≤ ∞, in the norm and almost everywhere. © 2019 Trudy Instituta Matematiki i Mekhaniki UrO RAN. All rights reserved.