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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.13460 |
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| _version_ | 1866910520461754368 |
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| author | Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Hasannasab, M. Quellmalz, M. Steidl, G. Teschke, G. |
| author_facet | Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Hasannasab, M. Quellmalz, M. Steidl, G. Teschke, G. |
| contents | In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a representation of the Lorentz group, which is square-integrable modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary and sufficient conditions for functions on the sphere, which ensure that the corresponding system is a frame. We strengthen a similar result in \cite{AV99} by providing a complete and detailed proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_13460 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited Dahlke, S. De Mari, F. De Vito, E. Hansen, M. Hasannasab, M. Quellmalz, M. Steidl, G. Teschke, G. Functional Analysis In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a representation of the Lorentz group, which is square-integrable modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary and sufficient conditions for functions on the sphere, which ensure that the corresponding system is a frame. We strengthen a similar result in \cite{AV99} by providing a complete and detailed proof. |
| title | Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2012.13460 |