Atomic decompositions of Besov spaces related to symmetric cones

TL;DR

This paper extends atomic decompositions of Besov spaces to general symmetric cones using wavelet theory, establishing isomorphisms with reproducing kernel spaces and enabling atomic decompositions through sampling.

Contribution

It introduces a wavelet-based approach for atomic decompositions of Besov spaces on symmetric cones, generalizing previous results from the light cone case.

Findings

Wavelet transforms create isomorphisms between Besov and kernel spaces

Sampling in the transformed domain yields atomic decompositions and frames

Extension from light cone to general symmetric cones achieved

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.