Coorbit Space Theory for Quasi-Banach Spaces

Details Coorbit Space Theory for Quasi-Banach Spaces Coorbit Space Theory for Quasi-Banach Spaces

2005-07-22

arxiv.org/abs/math/0507466v1

Mathematics

Functional Analysis

27 pages

Scientific paper

We generalize the classical coorbit space theory developed by Feichtinger and Gr"ochenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best $n$-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces $M^{p,q}_m$, $0< p,q \leq \infty$.

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