Localization of operator-valued frames
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908382508613632 |
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| author | Köhldorfer, Lukas Balazs, Peter |
| author_facet | Köhldorfer, Lukas Balazs, Peter |
| contents | We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of an operator-valued frame is preserved by its canonical dual. Moreover, we show that the series associated to the perfect reconstruction of an operator-valued frame converges not only in the underlying Hilbert space, but also in a whole class of associated (quasi-)Banach spaces. Finally, we apply our results to irregular Gabor g-frames. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization of operator-valued frames Köhldorfer, Lukas Balazs, Peter Functional Analysis We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of an operator-valued frame is preserved by its canonical dual. Moreover, we show that the series associated to the perfect reconstruction of an operator-valued frame converges not only in the underlying Hilbert space, but also in a whole class of associated (quasi-)Banach spaces. Finally, we apply our results to irregular Gabor g-frames. |
| title | Localization of operator-valued frames |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2503.24170 |