Gomez, JaimeGuerra, AndreRamos, Joao P. G.Tilli, Paolo2024-05-012024-05-012024-05-012024-03-0110.1007/s00222-024-01248-2https://infoscience.epfl.ch/handle/20.500.14299/207580WOS:001172462400001We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of positive, finite measure. We then show that an optimal power of the deficit controls both the -distance of to an appropriate class of Gaussians and the distance of to a ball, through the Fraenkel asymmetry of . Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context.Physical Sciencestext::journal::journal article::research article