Examples of Coorbit Spaces for Dual Pairs

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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. Gröchenig. 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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Functional Analysis, Representation Theory, 43A15, 42B35 (Primary) 22D12 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/168765

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.4120
 http://arxiv.org/abs/0711.4120

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arXiv