Hermite expansions for spaces of functions with nearly optimal time-frequency decay
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912420066230272 |
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| author | Neyt, Lenny Toft, Joachim Vindas, Jasson |
| author_facet | Neyt, Lenny Toft, Joachim Vindas, Jasson |
| contents | We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line satisfying \begin{equation*} |f(x)| \lesssim e^{-(\frac{1}{2} - λ) x^{2}} , \qquad | \widehat{f}(ξ)| \lesssim e^{-(\frac{1}{2} - λ) ξ^{2}} , \qquad \forall λ> 0 . \end{equation*} In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [J. Funct. Anal. 284 (2023), 109724]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hermite expansions for spaces of functions with nearly optimal time-frequency decay Neyt, Lenny Toft, Joachim Vindas, Jasson Functional Analysis 46E10, 42A38, 42C10, 30H20 We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line satisfying \begin{equation*} |f(x)| \lesssim e^{-(\frac{1}{2} - λ) x^{2}} , \qquad | \widehat{f}(ξ)| \lesssim e^{-(\frac{1}{2} - λ) ξ^{2}} , \qquad \forall λ> 0 . \end{equation*} In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [J. Funct. Anal. 284 (2023), 109724]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle. |
| title | Hermite expansions for spaces of functions with nearly optimal time-frequency decay |
| topic | Functional Analysis 46E10, 42A38, 42C10, 30H20 |
| url | https://arxiv.org/abs/2405.03282 |