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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12112 |
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| _version_ | 1866913357146095616 |
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| author | Gröchenig, Karlheinz Shafkulovska, Irina |
| author_facet | Gröchenig, Karlheinz Shafkulovska, Irina |
| contents | Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution.
We investigate the question which metaplectic Wigner distributions satisfy an uncertainty principle in the style of Benedicks and Amrein-Berthier. That is, if the metaplectic Wigner distribution is supported on a set of finite measure, must the functions then be zero? While this statement holds for the short-time Fourier transform, it is false for some other natural time-frequency representations. We provide a full characterization of the class of metaplectic Wigner distributions which exhibit an uncertainty principle of this type, both for sesquilinear and quadratic versions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Benedicks-type uncertainty principle for metaplectic time-frequency representations Gröchenig, Karlheinz Shafkulovska, Irina Functional Analysis 81S07, 81S30, 22E46 Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which metaplectic Wigner distributions satisfy an uncertainty principle in the style of Benedicks and Amrein-Berthier. That is, if the metaplectic Wigner distribution is supported on a set of finite measure, must the functions then be zero? While this statement holds for the short-time Fourier transform, it is false for some other natural time-frequency representations. We provide a full characterization of the class of metaplectic Wigner distributions which exhibit an uncertainty principle of this type, both for sesquilinear and quadratic versions. |
| title | Benedicks-type uncertainty principle for metaplectic time-frequency representations |
| topic | Functional Analysis 81S07, 81S30, 22E46 |
| url | https://arxiv.org/abs/2405.12112 |