[HTML][HTML] The uncertainty principle for the short-time Fourier transform on finite cyclic groups: cases of equality
F Nicola - Journal of Functional Analysis, 2023 - Elsevier
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 …
couple of functions f, g∈ ℓ 2 (ZN)∖{0}, the short-time Fourier transform V gf has support of …
The norm of time-frequency and wavelet localization operators
F Nicola, P Tilli - Transactions of the American Mathematical Society, 2023 - ams.org
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 …
d)\to L^ 2 (\mathbb {R}^ d) $, where $ F $ is a weight in $\mathbb {R}^{2d} $, were …
[HTML][HTML] Maximally localized Gabor orthonormal bases on locally compact Abelian groups
F Nicola - Advances in Mathematics, 2024 - Elsevier
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 …
basis of L 2 (A) that consists of time-frequency shifts of some template f∈ L 2 (A). It is well …
The norm of time-frequency and wavelet localization operators
F Nicola, P Tilli - arXiv preprint arXiv:2207.08624, 2022 - arxiv.org
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 …
d)\to L^ 2 (\mathbb {R}^ d) $, where $ F $ is a weight in $\mathbb {R}^{2d} $, were …
The Fefferman-Phong uncertainty principle for representations of Lie groups and applications
F Nicola - arXiv preprint arXiv:2402.03250, 2024 - arxiv.org
We prove a general uncertainty principle for square-integrable irreducible unitary
representations of connected Lie groups. The concentration of the matrix coefficients is …
representations of connected Lie groups. The concentration of the matrix coefficients is …
The quantitative isoperimetric inequality for the Hilbert-Schmidt norm of localization operators
F Nicola, F Riccardi - arXiv preprint arXiv:2401.04659, 2024 - arxiv.org
In this paper we study the Hilbert-Schmidt norm of time-frequency localization operators $ L_
{\Omega}\colon L^ 2 (\mathbb {R}^ d)\rightarrow L^ 2 (\mathbb {R}^ d) $, with Gaussian …
{\Omega}\colon L^ 2 (\mathbb {R}^ d)\rightarrow L^ 2 (\mathbb {R}^ d) $, with Gaussian …
Mutual estimates of time-frequency representations and uncertainty principles
AA Albanese, C Mele, A Oliaro - Annali di Matematica Pura ed Applicata …, 2024 - Springer
In this paper we give different estimates between Lebesgue norms of quadratic time-
frequency representations. We show that, in some cases, it is not possible to have such …
frequency representations. We show that, in some cases, it is not possible to have such …