On the Atomic Decomposition of Coorbit Spaces with Non-integrable Kernel
| Autor: | Gabriele Steidl, Gerd Teschke, Lukas Sawatzki, Stephan Dahlke, Filippo De Mari, Felix Voigtlaender, Ernesto De Vito |
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| Rok vydání: | 2019 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Smoothness (probability theory) Kernel (set theory) Group (mathematics) Context (language use) Smoothness spaces Function (mathematics) Atomic decompositions Banach frames Coorbit theory Group representations Smoothness spaces Group representation Banach frames Atomic decompositions Coorbit theory Group representations Representation (mathematics) Mathematics Haar measure |
| Zdroj: | Landscapes of Time-Frequency Analysis ISBN: 9783030052096 |
| Popis: | This chapter is concerned with recent progress in the context of coorbit space theory. Based on a square-integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a function is measured by the decay of the associated voice transform. Moreover, by discretizing the representation, atomic decompositions and Banach frames can be constructed. Usually, the whole machinery works well if the associated reproducing kernel is integrable with respect to a weighted Haar measure on the group. In recent studies, it has turned out that to some extent coorbit spaces can still be established if this condition is violated. In this chapter, we clarify in which sense atomic decompositions and Banach frames for these generalized coorbit spaces can be obtained. |
| Databáze: | OpenAIRE |
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