Atomic decompositions of Besov spaces related to symmetric cones

2013/03/12 by Jens Gerlach Christensen, Christensen, Jens Gerlach
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1303.2759

arxiv created 2013/03/12 · arxiv updated 2013/03/13

Abstract

In this paper we extend the atomic decompositions previously obtained for Besov spaces related to the forward light cone to general symmetric cones. We do so via wavelet theory adapted to the cone. The wavelet transforms sets up an isomorphism between the Besov spaces and certain reproducing kernel function spaces on the group, and sampling of the transformed data will provide the atomic decompositions and frames for the Besov spaces.

Related

• Atomic decompositions of mixed norm Bergman spaces on tube type domains
• Homogeneous Besov spaces on stratified Lie groups and their wavelet characterization
• From Frazier-Jawerth characterizations of Besov spaces to Wavelets and Decomposition spaces
• Vanishing moment conditions for wavelet atoms in higher dimensions
• Construction of Banach frames and atomic decompositions of anisotropic Besov spaces