2025/09/19 by Monika Dörfler, Lukas Köhldorfer, Dörfler, Monika +5 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Advanced Banach Space Theory #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2509.16440
Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \citedoelumcskr24 and \citeköbaLOC25, where one is based on the coorbit theory of Feichtinger-Gröchening while the other is based on the theory of localized frames. We show that for certain Gabor g-frames the co-orbit spaces in \citeköbaLOC25 conincide with the ones in \citedoelumcskr24 and we refer to this class of operators as operator coorbit spaces. Based on the description of operator coorbit spaces in terms of Gabor g-frames we provide operator dictionaries for these spaces that allow us to define sparsity classes in this setting. We establish that these sparsity classes also coincide with the operator coorbit spaces, which holds, in particular for all Feichtinger operators, a nice class of mixed states. Numerical examples confirm the expected approximation quality by few terms for appropriately chosen operators.