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Hermite expansions for spaces of functions with nearly optimal time-frequency decay

Lenny Neyt (UGent) , Joachim Toft and Jasson Vindas Diaz (UGent)
(2025) JOURNAL OF FUNCTIONAL ANALYSIS. 288(3).
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Abstract
We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line such that they and their Fourier transforms satisfy almost optimal Gaussian decay estimates. In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [21]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle.
Keywords
Functions with nearly optimal time-frequency decay, Bargmann transform, Phragmén-Lindelöf principle on sectors, Hermite series expansions, GELFAND-SHILOV SPACES, ULTRADIFFERENTIABLE FUNCTIONS, FOURIER

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Citation

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MLA
Neyt, Lenny, et al. “Hermite Expansions for Spaces of Functions with Nearly Optimal Time-Frequency Decay.” JOURNAL OF FUNCTIONAL ANALYSIS, vol. 288, no. 3, 2025, doi:10.1016/j.jfa.2024.110706.
APA
Neyt, L., Toft, J., & Vindas Diaz, J. (2025). Hermite expansions for spaces of functions with nearly optimal time-frequency decay. JOURNAL OF FUNCTIONAL ANALYSIS, 288(3). https://doi.org/10.1016/j.jfa.2024.110706
Chicago author-date
Neyt, Lenny, Joachim Toft, and Jasson Vindas Diaz. 2025. “Hermite Expansions for Spaces of Functions with Nearly Optimal Time-Frequency Decay.” JOURNAL OF FUNCTIONAL ANALYSIS 288 (3). https://doi.org/10.1016/j.jfa.2024.110706.
Chicago author-date (all authors)
Neyt, Lenny, Joachim Toft, and Jasson Vindas Diaz. 2025. “Hermite Expansions for Spaces of Functions with Nearly Optimal Time-Frequency Decay.” JOURNAL OF FUNCTIONAL ANALYSIS 288 (3). doi:10.1016/j.jfa.2024.110706.
Vancouver
1.
Neyt L, Toft J, Vindas Diaz J. Hermite expansions for spaces of functions with nearly optimal time-frequency decay. JOURNAL OF FUNCTIONAL ANALYSIS. 2025;288(3).
IEEE
[1]
L. Neyt, J. Toft, and J. Vindas Diaz, “Hermite expansions for spaces of functions with nearly optimal time-frequency decay,” JOURNAL OF FUNCTIONAL ANALYSIS, vol. 288, no. 3, 2025.
@article{01JD0R8978PFNY6WAMFD1MY2QN,
  abstract     = {{We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line such that they and their Fourier transforms satisfy almost optimal Gaussian decay estimates.
In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in [21]. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle.}},
  articleno    = {{110706}},
  author       = {{Neyt, Lenny and Toft, Joachim and Vindas Diaz, Jasson}},
  issn         = {{0022-1236}},
  journal      = {{JOURNAL OF FUNCTIONAL ANALYSIS}},
  keywords     = {{Functions with nearly optimal time-frequency decay,Bargmann transform,Phragmén-Lindelöf principle on sectors,Hermite series expansions,GELFAND-SHILOV SPACES,ULTRADIFFERENTIABLE FUNCTIONS,FOURIER}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{17}},
  title        = {{Hermite expansions for spaces of functions with nearly optimal time-frequency decay}},
  url          = {{http://doi.org/10.1016/j.jfa.2024.110706}},
  volume       = {{288}},
  year         = {{2025}},
}
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