Examples of Coorbit Spaces for Dual Pairs
| Autor: | Jens Gerlach Christensen, Gestur Ólafsson |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Mathematics::Functional Analysis
Discrete series representation Applied Mathematics 010102 general mathematics Banach space 010103 numerical & computational mathematics 01 natural sciences Algebra Bergman space Besov space Interpolation space Locally compact space 0101 mathematics Lp space Representation (mathematics) Mathematics |
| Zdroj: | Acta Applicandae Mathematicae. 107:25-48 |
| ISSN: | 1572-9036 0167-8019 |
| DOI: | 10.1007/s10440-008-9390-4 |
| Popis: | 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. Grochenig. 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 SL2(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. |
| Databáze: | OpenAIRE |
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