59 citations · 159 across the 37 of their papers we have counts for
42 papers
Modulation spaces: from Feichtinger's original definition to modern Gabor and symplectic characterizations
Antonio Caputo, Elena Cordero, Gianluca Giachi +1
We present an expository excursus on modulation spaces, from Feichtinger's original construction on locally compact abelian groups to recent symplectic formulations. We trace the s…
The filter of singularities in global anisotropic microlocal analysis
Luigi Rodino, Patrik Wahlberg
We define a filter of time-frequency anisotropic global singularities of phase space for tempered distributions. The filter contains information from the corresponding anisotropic…
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…
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…
Propagation of singularities for anharmonic Schrödinger equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We consider evolution equations for two classes of generalized anharmonic oscillators and the associated initial value problem in the space of tempered distributions. We prove that…
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…
Propagation of anisotropic Gabor singularities for Schrödinger type equations
Marco Cappiello, Luigi Rodino, Patrik Wahlberg
We show results on propagation of anisotropic Gabor wave front sets for solutions to a class of evolution equations of Schrödinger type. The Hamiltonian is assumed to have a real-v…
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…
Anisotropic global microlocal analysis for tempered distributions
Luigi Rodino, Patrik Wahlberg
We study an anisotropic version of the Shubin calculus of pseudodifferential operators on . Anisotropic symbols and Gabor wave front sets are defined in terms of decay…
Characterization of modulation spaces by symplectic representations and applications to Schrödinger equations
Elena Cordero, Luigi Rodino
In the last twenty years modulation spaces, introduced by H. G. Feichtinger in 1983, have been successfully addressed to the study of signal analysis, PDE's, pseudodifferential ope…
Microlocal analysis for Gelfand--Shilov spaces
Luigi Rodino, Patrik Wahlberg
We introduce an anisotropic global wave front set of Gelfand--Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the l…
Wigner analysis of operators. Part I: pseudodifferential operators and wave fronts
Elena Cordero, Luigi Rodino
We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the -\emph…
An introduction to the Gabor wave front set
Luigi Rodino, S. Ivan Trapasso
In this expository note we present an introduction to the Gabor wave front set. As is often the case, this tool in microlocal analysis has been introduced and reinvented in differe…
Anisotropic Shubin operators and eigenfunctions expansions in Gelfand-Shilov spaces
Marco Cappiello, Todor Gramchev, Stevan Pilipovic +1
We derive new results on the characterization of Gelfand--Shilov spaces , , by Gevrey estimates of the norms of iterates of …
Gabor analysis for Schrodinger equations and propagation of singularities
Elena Cordero, Fabio Nicola, Luigi Rodino
We consider the Schrödinger equation \begin{equation*} i \displaystyle\frac{\partial u}{\partial t} +Hu=0,\quad H=a(x,D), \end{equation*} where the Hamiltonian , , i…
Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians
Karel Pravda-Starov, Luigi Rodino, Patrik Wahlberg
We study propagation of the Gabor wave front set for a Schrödinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. We poi…
Propagation of singularities for semilinear Schrödinger equations
Fabio Nicola, Luigi Rodino
We study the propagation of singularities for semilinear Schrodinger equations with quadratic Hamiltonians, in particular for the semilinear harmonic oscillator. We show that the p…
Gabor wave packets and evolution operators
Elena Cordero, Fabio Nicola, Luigi Rodino
We perform a Gabor analysis for a large class of evolution equations with constant coefficients. We show that the corresponding propagators have a very sparse Gabor matrix, display…
Integral Representations for the Class of Generalized Metaplectic Operators
E. Cordero, F. Nicola, L. Rodino
This article gives explicit integral formulas for the so-called generalized metaplectic operators, i.e. Fourier integral operators (FIOs) of Schrödinger type, having a symplectic m…