This is an announcement for the paper "Coorbit spaces for dual pairs" by J. G. Christensen and G. Olafsson.

Abstract: This paper contains a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Groechenig. This theory has been a powerful tool in characterizing Banach spaces of functions 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 suggest a generalization of the coorbit space theory, which is able to account for a wider range of Banach spaces and also for quasi Banach spaces. A few examples of Banach spaces which could not be covered by the previous theory are described.

Archive classification: math.FA math.RT

Mathematics Subject Classification: 43A15,42B35 (Primary) 22D12 (Secondary)

The source file(s), coorbit.bbl: 4205 bytes

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0711.4120

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http://arXiv.org/abs/0711.4120

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