Mutual estimates of time-frequency representations and uncertainty principles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917599481167872 |
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| author | Albanese, Angela A. Mele, Claudio Oliaro, Alessandro |
| author_facet | Albanese, Angela A. Mele, Claudio Oliaro, Alessandro |
| contents | In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutual estimates of time-frequency representations and uncertainty principles Albanese, Angela A. Mele, Claudio Oliaro, Alessandro Functional Analysis 42B10, 46F05, 46E30, 46F12 In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations. |
| title | Mutual estimates of time-frequency representations and uncertainty principles |
| topic | Functional Analysis 42B10, 46F05, 46E30, 46F12 |
| url | https://arxiv.org/abs/2402.17578 |