Localized frames without inequalities
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918054428934144 |
|---|---|
| author | Balazs, Peter Köhldorfer, Lukas Speckbacher, Michael |
| author_facet | Balazs, Peter Köhldorfer, Lukas Speckbacher, Michael |
| contents | We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the frame property and nine conditions that do not involve any inequalities. This is done by studying the properties of their frame-related operators on the co-orbit spaces generated by the reference Riesz basis. We apply our main result to the setting of shift-invariant spaces and obtain new conditions for stable sets of sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localized frames without inequalities Balazs, Peter Köhldorfer, Lukas Speckbacher, Michael Functional Analysis We consider countable families of vectors in a separable Hilbert space, which are mutually localized with respect to a fixed localized Riesz basis. We prove the equivalence of the frame property and nine conditions that do not involve any inequalities. This is done by studying the properties of their frame-related operators on the co-orbit spaces generated by the reference Riesz basis. We apply our main result to the setting of shift-invariant spaces and obtain new conditions for stable sets of sampling. |
| title | Localized frames without inequalities |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.02862 |