Examples of Coorbit Spaces for Dual Pairs

Details Examples of Coorbit Spaces for Dual Pairs Examples of Coorbit Spaces for Dual Pairs

2007-11-26

arxiv.org/abs/0711.4120v2

Mathematics

Functional Analysis

Scientific paper

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\"ochenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterization of some Bergman spaces by the discrete series representation of $\mathrm{SL}_2(\mathbb{R})$. We present examples of Banach spaces which could not be covered by the previous theory, and we also provide atomic decompositions for an example related to a non-integrable representation.

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