Excursus on modulation spaces via metaplectic operators and related time-frequency representations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914728110981120 |
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| author | Cordero, Elena Giacchi, Gianluca |
| author_facet | Cordero, Elena Giacchi, Gianluca |
| contents | Modulation spaces were originally introduced by Feichtinger in 1983. Since the 2000s there have been thousands of contributions using them as correct framework; they range from PDEs, pseudodifferential operators, quantum mechanics, signal analysis. This justifies a deep study of such spaces and the related Wiener ones. Recently, metaplectic Wigner distributions, which contain as special examples the $τ$-Wigner distributions, the ambiguity function and the Short-time Fourier transform, have proved to characterize modulation spaces, under suitable assumptions. We investigate the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. We add a new result on this topic and conclude with an exhaustive vision of these characterizations. Similar results hold for the Wiener amalgam ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13166 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Excursus on modulation spaces via metaplectic operators and related time-frequency representations Cordero, Elena Giacchi, Gianluca Analysis of PDEs 42C15, 42B35, 42A38 Modulation spaces were originally introduced by Feichtinger in 1983. Since the 2000s there have been thousands of contributions using them as correct framework; they range from PDEs, pseudodifferential operators, quantum mechanics, signal analysis. This justifies a deep study of such spaces and the related Wiener ones. Recently, metaplectic Wigner distributions, which contain as special examples the $τ$-Wigner distributions, the ambiguity function and the Short-time Fourier transform, have proved to characterize modulation spaces, under suitable assumptions. We investigate the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. We add a new result on this topic and conclude with an exhaustive vision of these characterizations. Similar results hold for the Wiener amalgam ones. |
| title | Excursus on modulation spaces via metaplectic operators and related time-frequency representations |
| topic | Analysis of PDEs 42C15, 42B35, 42A38 |
| url | https://arxiv.org/abs/2305.13166 |