10 papers
Approximation Rates for Metaplectic Neural Networks
Ahmed Abdeljawad, Marcello Carioni, Elena Cordero
In this paper we develop quantitative approximation results for shallow neural networks constructed using a dictionary based on metaplectic operators. First, we extend the concept…
Time-Frequency Analysis for Neural Networks
Ahmed Abdeljawad, Elena Cordero
We develop a quantitative approximation theory for shallow neural networks using tools from time-frequency analysis. Working in weighted modulation spaces $M^{p,q}_m(\mathbf{R}^{d}…
Beyond Single-Window Graph Fourier Analysis
Iulia Martina Bulai, Elena Cordero, Edoardo Pucci +1
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulati…
Anisotropic uncertainty principles for metaplectic operators
Elena Cordero, Gianluca Giacchi, Edoardo Pucci
We establish anisotropic uncertainty principles (UPs) for general metaplectic operators acting on , including degenerate cases associated with symplectic matrice…
Wigner and Gabor phase-space analysis of propagators for evolution equations
Elena Cordero, Gianluca Giacchi, Luigi Rodino
We study the Wigner kernel and the Gabor matrix associated with the propagators of a broad class of linear evolution equations, including the complex heat, wave, and Hermite equati…
Sparse Gabor representations of metaplectic operators: controlled exponential decay and Schrödinger confinement
Elena Cordero, Gianluca Giacchi, Edoardo Pucci +1
Motivated by the phase space analysis of Schrödinger evolution operators, in this paper we investigate how metaplectic operators are approximately diagonalized along the correspon…