On wavelet coorbit spaces associated to different dilation groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916479261212672 |
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| author | Führ, Hartmut van Velthoven, Jordy Timo Voigtlaender, Felix |
| author_facet | Führ, Hartmut van Velthoven, Jordy Timo Voigtlaender, Felix |
| contents | This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to both irreducible and reducible quasi-regular representations. We show that the use of reducible representations is essential to include a variety of examples, such as anisotropic Besov spaces defined by general expansive matrices, in a common framework. The obtained criteria yield, among others, a simple characterization of subgroups of a dilation group yielding the same coorbit spaces. They also allow to clarify which anisotropic Besov spaces have an alternative description as coorbit spaces associated to irreducible quasi-regular representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On wavelet coorbit spaces associated to different dilation groups Führ, Hartmut van Velthoven, Jordy Timo Voigtlaender, Felix Functional Analysis Classical Analysis and ODEs This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to both irreducible and reducible quasi-regular representations. We show that the use of reducible representations is essential to include a variety of examples, such as anisotropic Besov spaces defined by general expansive matrices, in a common framework. The obtained criteria yield, among others, a simple characterization of subgroups of a dilation group yielding the same coorbit spaces. They also allow to clarify which anisotropic Besov spaces have an alternative description as coorbit spaces associated to irreducible quasi-regular representations. |
| title | On wavelet coorbit spaces associated to different dilation groups |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.08416 |