Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region

Aleksei Kulikov

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arXiv · 2306.12430

Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region

Aleksei Kulikov

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Abstract

We prove that the eigenvalues $\lambda_n(c)$ of the time-frequency localization operator satisfy $\lambda_n(c) > 1 - \delta^c$ for $n = [(1-\varepsilon)c]$, where $\delta = \delta(\varepsilon) < 1$ and $\varepsilon > 0$ is arbitrary, improving on the result of Bonami, Jaming and Karoui, who proved it for $\varepsilon \ge 0.42$. The proof is based on the properties of the Bargmann transform.

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BibTeX RIS

Aleksei Kulikov. 2023-06-03. Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region. https://arxiv.org/abs/2306.12430

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