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We prove a conjecture by Vemuri [Hermite expansions and Hardy's theorem, arXiv:0801.2234, 2008] by proving sharp bounds on l(kappa) sums of Hermite functions multiplied by an exponentially decaying factor. More explicitly, we prove that, for each y > 0, we ...
We 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 pos ...
We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...
