On Coorbit Fréchet Spaces
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915686427656192 |
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| author | Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Steidl, G. Teschke, G. |
| author_facet | Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Steidl, G. Teschke, G. |
| contents | This paper is concerned with a new approach to coorbit space theory. Usually, coorbit spaces are defined by collecting all distributions for which the voice transform associated with a square-integrable group representation possesses a certain decay, usually measured in a Banach space norm such as weighted $L_p$-norms. Unfortunately, in cases where the representation does not satisfy certain integrability conditions, one is faced with a bottleneck, namely that the discretization of the coorbit spaces is surprisingly difficult. It turns out that in these cases the construction of coorbit spaces as Fréchet spaces is much more convenient since then atomic decompositions can be established in a very natural way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Coorbit Fréchet Spaces Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Steidl, G. Teschke, G. Functional Analysis 41A30, 46E3, 46A04, 42C15 This paper is concerned with a new approach to coorbit space theory. Usually, coorbit spaces are defined by collecting all distributions for which the voice transform associated with a square-integrable group representation possesses a certain decay, usually measured in a Banach space norm such as weighted $L_p$-norms. Unfortunately, in cases where the representation does not satisfy certain integrability conditions, one is faced with a bottleneck, namely that the discretization of the coorbit spaces is surprisingly difficult. It turns out that in these cases the construction of coorbit spaces as Fréchet spaces is much more convenient since then atomic decompositions can be established in a very natural way. |
| title | On Coorbit Fréchet Spaces |
| topic | Functional Analysis 41A30, 46E3, 46A04, 42C15 |
| url | https://arxiv.org/abs/2512.17502 |