11 papers
On the existence of extremizers for the sum of eigenvalues of Toeplitz operators
Fabio Nicola, Federico Riccardi, Paolo Tilli
We prove that, among all measurable sets of prescribed Lebesgue measure, there exists a set maximizing the sum of the first eigenvalues () of the…
A Phase Space Criterion for Dynamical Amrein-Berthier Uncertainty
Piero D'Ancona, Diego Fiorletta, Fabio Nicola
We prove a phase space criterion for dynamical Amrein-Berthier uncertainty principles. The abstract result says that, for a Fourier integral operator associated with…
An elementary approach to Wehrl-type entropy bounds in quantitative form
Fabio Nicola, Federico Riccardi, Paolo Tilli
We consider the problem of the stability (with sharp exponent) of the Lieb--Solovej inequality for symmetric coherent states, which was obtained only recently by the author…
The Hudson theorem in LCA groups and infinite quantum spin systems
Fabio Nicola, Federico Riccardi
The celebrated Hudson theorem states that the Gaussian functions in are the only functions whose Wigner distribution is everywhere positive. Motivated by quantum inf…
Dynamical restriction for Schrödinger equations
Fabio Nicola
We prove a dynamical restriction principle, asserting that every restriction estimate satisfied by the Fourier transform in is also valid for the propagator of certa…
A life in Mathematical Analysis: a conversation with Luigi Rodino
Fabio Nicola
This note is the transcription of an interview with Professor Luigi Rodino, on the occasion of the ISAAC-ICMAM Conference of Analysis in Developing Countries (December 2, 2024 - Bo…
The isoperimetric inequality for partial sums of Toeplitz eigenvalues in the Fock space
Fabio Nicola, Federico Riccardi, Paolo Tilli
We prove that, among all subsets having circular symmetry and prescribed measure, the ball is the only maximizer of the sum of the first eigenvalues ($K\g…
The Wehrl-type entropy conjecture for symmetric coherent states: cases of equality and stability
Fabio Nicola, Federico Riccardi, Paolo Tilli
Lieb and Solovej proved that, for the symmetric representations, the corresponding Wehrl-type entropy is minimized by symmetric coherent states. However, the uniqueness of…
The wave function of stabilizer states and the Wehrl conjecture
Fabio Nicola
We focus on quantum systems represented by a Hilbert space , where is a locally compact Abelian group that contains a compact open subgroup. We examine two interconnect…
The Fefferman-Phong uncertainty principle for representations of Lie groups and applications
Fabio Nicola
The Fefferman-Phong uncertainty principle is a deep result concerning the order of magnitude of the bottom of the spectrum of second order pseudodifferential operators with nonnega…
The quantitative isoperimetric inequality for the Hilbert-Schmidt norm of localization operators
Fabio Nicola, Federico Riccardi
In this paper we study the Hilbert-Schmidt norm of time-frequency localization operators , with Gaussian window, associa…