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 study the eigenvalues and eigenfunctions of the time-frequency localization operator $
H_\Omega $ on a domain $\Omega $ of the time-frequency plane. The eigenfunctions are …

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 …

We obtain estimates for the L p-norm of the short-time Fourier transform (STFT) for functions
in modulation spaces, providing information about the concentration on a given subset of R …

We develop a quantum harmonic analysis framework for the affine group. This encapsulates
several examples in the literature such as affine localization operators, covariant integral …

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 …

We study mixed-state localization operators from the perspective of Werner's operator
convolutions which allows us to extend known results from the rank-one case to trace class …

Recently we introduced mixed-state localization operators associated with a density
operator and a (compact) domain in phase space. We continue the investigations of their …

We study sharp frame bounds of Gabor frames for integer redundancy with the standard
Gaussian window and prove that the square lattice optimizes both the lower and the upper …

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 …