Approximation properties of operator coorbit spaces and sparsity classes
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918144820379648 |
|---|---|
| author | Dörfler, Monika Köhldorfer, Lukas Luef, Franz McNulty, Henry |
| author_facet | Dörfler, Monika Köhldorfer, Lukas Luef, Franz McNulty, Henry |
| contents | Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{köbaLOC25}, where one is based on the coorbit theory of Feichtinger-Gröchening while the other is based on the theory of localized frames. We show that for certain Gabor g-frames the co-orbit spaces in \cite{köbaLOC25} conincide with the ones in \cite{doelumcskr24} and we refer to this class of operators as operator coorbit spaces. Based on the description of operator coorbit spaces in terms of Gabor g-frames we provide operator dictionaries for these spaces that allow us to define sparsity classes in this setting. We establish that these sparsity classes also coincide with the operator coorbit spaces, which holds, in particular for all Feichtinger operators, a nice class of mixed states. Numerical examples confirm the expected approximation quality by few terms for appropriately chosen operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation properties of operator coorbit spaces and sparsity classes Dörfler, Monika Köhldorfer, Lukas Luef, Franz McNulty, Henry Functional Analysis Extensions of coorbit spaces for functions to operators have been introduced by two different groups in \cite{doelumcskr24} and \cite{köbaLOC25}, where one is based on the coorbit theory of Feichtinger-Gröchening while the other is based on the theory of localized frames. We show that for certain Gabor g-frames the co-orbit spaces in \cite{köbaLOC25} conincide with the ones in \cite{doelumcskr24} and we refer to this class of operators as operator coorbit spaces. Based on the description of operator coorbit spaces in terms of Gabor g-frames we provide operator dictionaries for these spaces that allow us to define sparsity classes in this setting. We establish that these sparsity classes also coincide with the operator coorbit spaces, which holds, in particular for all Feichtinger operators, a nice class of mixed states. Numerical examples confirm the expected approximation quality by few terms for appropriately chosen operators. |
| title | Approximation properties of operator coorbit spaces and sparsity classes |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.16440 |