CONSTRUCTIONS OF MRA-BASED WAVELETS AND FRAMES IN WALSH ANALYSIS
Yu. A. Farkov · Poincare Journal of Analysis and Applications · 2015
In this paper, we review the basic constructions of MRA-based orthogonal wavelets and tight frames related to the generalized Walsh functions.Several differences between the constructed wavelets and the classical wavelets are indicated.Further, for any integer p ≥ 2, all compactly supported step refinable functions on the Vilenkin group G p are characterized.In addition, we include references to the following topics: biorthogonal wavelets on G p , approximation properties of compactly supported orthogonal wavelets and frames on the Vilenkin/Cantor groups, unconditional convergence of wavelet expansions, nonstationary, periodic, and discrete wavelets in Walsh analysis, p-multiresolution analysis on the positive half-line, and related subjects.