59 citations · 398 across the 59 of their papers we have counts for
35 papers · 1 filter
Maximally localized Gabor orthonormal bases on locally compact Abelian groups
Fabio Nicola
A Gabor orthonormal basis, on a locally compact Abelian (LCA) group , is an orthonormal basis of which consists of time-frequency shifts of some template .…
Stability of the scattering transform for deformations with minimal regularity
Fabio Nicola, S. Ivan Trapasso
Within the mathematical analysis of deep convolutional neural networks, the wavelet scattering transform introduced by Stéphane Mallat is a unique example of how the ideas of multi…
The uncertainty principle for the short-time Fourier transform on finite cyclic groups: cases of equality
Fabio Nicola
A well-known version of the uncertainty principle on the cyclic group states that for any couple of functions , the short-t…
Generalized moduli of continuity under irregular or random deformations via multiscale analysis
Fabio Nicola, S. Ivan Trapasso
Motivated by the problem of robustness to deformations of the input for deep convolutional neural networks, we identify signal classes which are inherently stable to irregular defo…
Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness
Divyang G. Bhimani, Ramesh Manna, Fabio Nicola +2
We study the Hermite operator in and its fractional powers , in phase space. Namely, we represent functions via the so-called short-time…
Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators
Elena Cordero, Fabio Nicola, S. Ivan Trapasso
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and…