59 citations · 159 across the 37 of their papers we have counts for
26 papers · 1 filter
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…
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…
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…
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…
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…
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…
Schrödinger equations with rough Hamiltonians
Elena Cordero, Fabio Nicola, Luigi Rodino
We consider a class of linear Schrödinger equations in R^d with rough Hamiltonian, namely with certain derivatives in the Sjöstrand class . We prove that the correspo…
Wave packet analysis of Schrodinger equations in analytic function spaces
Elena Cordero, Fabio Nicola, Luigi Rodino
We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generali…
Propagation of the Gabor Wave Front Set for Schrödinger Equations with non-smooth potentials
Elena Cordero, Fabio Nicola, Luigi Rodino
We consider Scrödinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may be not even differentiable. The well…
On the inverse to the harmonic oscillator
Marco Cappiello, Luigi Rodino, Joachim Toft
Let be the Weyl symbol of the inverse to the harmonic oscillator on . We prove that and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov typ…
Generalized Metaplectic Operators and the Schrödinger Equation with a Potential in the Sjöstrand Class
Elena Cordero, Karlheinz Gröchenig, Fabio Nicola +1
It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra g…
Decay estimates for solutions of nonlocal semilinear equations
Marco Cappiello, Todor Gramchev, Luigi Rodino
We investigate the decay for of weak Sobolev type solutions of semilinear nonlocal equations . We consider the case when is an elliptic Fo…
A Two Dimensional Adler-Manin Trace and Bi-singular Operators
Farzad Fathizadeh, Masoud Khalkhali, Fabio Nicola +1
Motivated by the theory of bi-singular pseudodifferential operators, we introduce a two dimensional version of the Adler-Manin trace. Our construction is rather general in the sens…