In this paper we solve an open problem concerning the characterization of those
measurable sets Ω⊂ R 2 d that, among all sets having a prescribed Lebesgue measure, can …

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 δ (f; Ω) which measures by how …

The objective of audio inpainting is to fill a gap in an audio signal. This is ideally done by
reconstructing the original signal or, at least, by inferring a meaningful surrogate signal. We …

For some special window functions ψ α∈ H 2 (C+) ψ_α∈H^2(C^+), we prove that, over all
sets Δ⊂ C+ Δ⊂C^+ of fixed hyperbolic measure ν (Δ) ν(Δ), those for which the Wavelet …

A well-known version of the uncertainty principle on the cyclic group ZN states that for any
couple of functions f, g∈ ℓ 2 (ZN)∖{0}, the short-time Fourier transform V gf has support of …

We study the fractal uncertainty principle in the joint time-frequency representation, and we
prove a version for the Short-Time Fourier transform with Gaussian window on the …

Time-frequency localization operators (with Gaussian window) $ L_F: L^ 2 (\mathbb {R}^
d)\to L^ 2 (\mathbb {R}^ d) $, where $ F $ is a weight in $\mathbb {R}^{2d} $, were …

A Gabor orthonormal basis, on a locally compact Abelian (LCA) group A, is an orthonormal
basis of L 2 (A) that consists of time-frequency shifts of some template f∈ L 2 (A). It is well …

In this paper we provide an optimal estimate for the operator norm of time-frequency
localization operators LF, φ: L 2 (R d)→ L 2 (R d), with Gaussian window φ and weight F …

We develop an alternative approach to the study of Fourier series, based on the Short-Time-
Fourier Transform (STFT) acting on $ L_ {\nu}^{2}(0, 1) $, the space of measurable functions …