Zobrazeno 1 - 10
of 150
pro vyhledávání: '"Tilli, Paolo"'
Lieb and Carlen have shown that mixed states with minimal Wehrl entropy are coherent states. We prove that mixed states with almost minimal Wehrl entropy are almost coherent states. This is proved in a quantitative sense where both the norm and the e
Externí odkaz:
http://arxiv.org/abs/2307.14089
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 $\delta(f;\Omega)$ which measures by how much the STFT of a function $f\in L^2(\mathbb R)$ fails to be o
Externí odkaz:
http://arxiv.org/abs/2307.09304
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we deduce contr
Externí odkaz:
http://arxiv.org/abs/2212.14008
Autor:
Nicola, Fabio, Tilli, Paolo
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 introduced in signal processing by I. Daubechies in 1988, inaugurating a new, geometric, phase
Externí odkaz:
http://arxiv.org/abs/2207.08624
Autor:
Ramos, João P. G., Tilli, Paolo
For some special window functions $\psi_{\beta} \in H^2(\mathbb{C}^+),$ we prove that, over all sets $\Delta \subset \mathbb{C}^+$ of fixed hyperbolic measure $\nu(\Delta),$ the ones over which the Wavelet transform $W_{\overline{\psi_{\beta}}}$ with
Externí odkaz:
http://arxiv.org/abs/2205.07998
We investigate the relations between normalized critical points of the nonlinear Schr\"odinger energy functional and critical points of the corresponding action functional on the associated Nehari manifold. Our first general result is that the ground
Externí odkaz:
http://arxiv.org/abs/2107.08655
Autor:
Nicola, Fabio, Tilli, Paolo
Publikováno v:
Invent. Math. 230 (2022), no. 1, 1--30
In this paper we solve an open problem concerning the characterization of those measurable sets $\Omega\subset \mathbb{R}^{2d}$ that, among all sets having a prescribed Lebesgue measure, can trap the largest possible energy fraction in time-frequency
Externí odkaz:
http://arxiv.org/abs/2106.03423
We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are obtained as weak limits of minimizers of a family of perturbed functi
Externí odkaz:
http://arxiv.org/abs/2004.13638
We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schr\"odinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS equation is con
Externí odkaz:
http://arxiv.org/abs/2004.07292
Autor:
Tilli, Paolo, Zucco, Davide
We study the optimal partitioning of a (possibly unbounded) interval of the real line into $n$ subintervals in order to minimize the maximum of certain set-functions, under rather general assumptions such as continuity, monotonicity, and a Radon-Niko
Externí odkaz:
http://arxiv.org/abs/1905.02432