Construction of Banach frames and atomic decompositions of anisotropic Besov spaces

2020/06/05 by Bytchenkoff, Dimitri
#42B35 #42C15 #42C40 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2006.03727

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.

Related

• A classification of anisotropic Besov spaces
• Embeddings of anisotropic Besov spaces into Sobolev spaces
• Atomic decompositions of Besov spaces related to symmetric cones
• Approximative K-Atomic Decompositions and frames in Banach Spaces
• Generalized Besov-type and Triebel-Lizorkin-type spaces