23 citations · 96 across the 23 of their papers we have counts for
24 papers
Pitt Inequalities and Logarithmic-type Uncertainty Principles for Metaplectic Operators
Gianluca Giacchi, Itamar Oliveira, Amy Tierney
In this work, we provide a complete characterisation of Pitt's inequality for metaplectic operators. The symplectic geometry underlying a metaplectic operator distinguishes effecti…
A Schrödinger characterization of the oscillator semigroup
Gianluca Giacchi
The oscillator (or metaplectic) semigroup is classically defined as the two-fold cover of the semigroup of positive complex symplectic matrices. Although geometrically precise, thi…
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…
The metaplectic semigroup and its applications to time-frequency analysis and evolution operators
Gianluca Giacchi, Luigi Rodino, Davide Tramontana
We develop a systematic analysis of the metaplectic semigroup associated with positive complex symplectic matrices, a notion introduced almost simulta…
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…
On the microlocal phase-space concentration of Wigner distributions associated with Schrödinger evolutions
Gianluca Giacchi, Davide Tramontana
In this work, we investigate the microlocal properties of the evolutions of Schrödinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaple…
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 correspond…
Bespoke multiresolution analysis of graph signals
Giacomo Elefante, Gianluca Giacchi, Michael Multerer +1
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framewor…
Multiresolution local smoothness detection in non-uniformly sampled multivariate signals
Sara Avesani, Gianluca Giacchi, Michael Multerer
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly samp…
Metaplectic operators with quasi-diagonal kernels
Gianluca Giacchi, Luigi Rodino
Metaplectic operators form a relevant class of operators appearing in different applications, in the present work we study their Schwartz kernels. Namely, diagonality of a kernel i…
Wigner analysis of operators. Part III: Controlling ghost frequencies
Elena Cordero, Gianluca Giacchi, Luigi Rodino
The integration of operator kernels with the Wigner distribution, first conceptualized by E. Wigner in 1932 and later extended by L. Cohen and others, has opened new avenues in tim…
Hardy's Uncertainty principle for Schrödinger equations with quadratic Hamiltonians
Elena Cordero, Gianluca Giacchi, Eugenia Malinnikova
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in and its Fourier transform cannot both decay arbitrarily fas…
Understanding of linear operators through Wigner analysis
Elena Cordero, Gianluca Giacchi, Edoardo Pucci
In this work, we extend Wigner's original framework to analyze linear operators by examining the relationship between their Wigner and Schwartz kernels. Our approach includes the i…
Wigner kernel and Gabor matrix of operators
Elena Cordero, Gianluca Giacchi, Luigi Rodino
We exhibit the connection between the Wigner kernel and the Gabor matrix of a linear bounded operator T : . The smoothing…
Wigner Analysis of Fourier Integral Operators with symbols in the Shubin classes
Elena Cordero, Gianluca Giacchi, Luigi Rodino +1
We study the decay properties of Wigner kernels for Fourier integral operators of types I and II. The symbol spaces that allow a nice decay of these kernels are the Shubin classes…
A Unified Approach to Time-Frequency Representations and Generalized Spectrogram
Elena Cordero, Gianluca Giacchi, Luigi Rodino
To overcome the impossibility of representing the energy of a signal simultaneously in time and frequency, many time-frequency representations have been introduced in the literatur…
Wigner Representation of Schrödinger Propagators
Elena Cordero, Gianluca Giacchi, Luigi Rodino
We perform a Wigner analysis of Fourier integral operators (FIOs), whose main examples are Schrödinger propagators arising from quadratic Hamiltonians with bounded perturbations. T…
Excursus on modulation spaces via metaplectic operators and related time-frequency representations
Elena Cordero, Gianluca Giacchi
Modulation spaces were originally introduced by Feichtinger in 1983. Since the 2000s there have been thousands of contributions using them as correct framework; they range from PDE…
Metaplectic Gabor frames of Wigner-Decomposable Distributions
Elena Cordero, Gianluca Giacchi
Metaplectic Wigner distributions generalize the most popular time-frequency representations, such as the short-time Fourier transform (STFT) and -Wigner distributions, using met…
Metaplectic Gabor Frames and Symplectic Analysis of Time-Frequency Spaces
Elena Cordero, Gianluca Giacchi
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we devel…
Symplectic Analysis of Time-Frequency Spaces
Elena Cordero, Gianluca Giacchi
We present a different symplectic point of view in the definition of weighted modulation spaces and weighted Wiener amalgam spaces $W(\mathcal{F} L^p_{m_1…
On the determination of Lagrange Multipliers for a weighted LASSO problem using geometric and convex analysis techniques
Gianluca Giacchi, Bastien Milani, Benedetta Franchieschiello
Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients. Its applications span…
Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators
Elena Cordero, Gianluca Giacchi
We generalize the results for Banach algebras of pseudodifferential operators obtained by Gröchenig and Rzeszotnik in [24] to quasi-algebras of Fourier integral operators. Namely,…
Wigner Analysis of Operators. Part II: Schrödinger equations
Elena Cordero, Gianluca Giacchi, Luigi Rodino
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schrödinger equations with bounded perturbations. To reach this go…