Construction of Banach frames and atomic decompositions of anisotropic Besov spaces

TL;DR

This paper develops a framework for constructing Banach frames and atomic decompositions for anisotropic Besov spaces using generalized shift-invariant systems, expanding the tools available for analyzing these function spaces.

Contribution

It introduces a method to generate Banach frames and atomic decompositions for anisotropic Besov spaces via shift-invariant systems based on any expansive matrix.

Findings

Established conditions for systems to form Banach frames

Provided criteria for atomic decompositions in anisotropic Besov spaces

Extended the decomposition method to anisotropic settings

Abstract

We construct generalised shift-invariant systems of functions of several real variables for anisotropic Besov spaces that can be generated by the decomposition method using any given expansive matrix and establish the conditions on those systems under which they will constitute Banach frames or sets of atoms for the anisotropic homo- or inhomogeneous Besov spaces.