Stability of the Faber-Krahn inequality for the short-time Fourier transform

par André Guerra (ETH Zürich)

lundi 9 oct. 2023, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

For a given signal, its short-time Fourier transform (STFT) is a measure of its "instantaneous frequency". For generic signals, however, the uncertainty principle says that the concept of instantaneous frequency is not well defined and thus the STFT can only be so much concentrated on a given set of finite, positive measure. The Faber-Krahn inequality for the STFT asserts that the STFT is optimally localized if the localization domain is a ball and the signal is a suitable Gaussian. In this talk we will discuss a recent proof of an optimal, quantitative version of this result, joint with J. Gómez, J. P. G. Ramos and P. Tilli.