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Analisi microlocale e tempo-frequenza

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  • Description
  • Report 2013
  • Report 2014


This group is concerned with the research on microlocal and time-frequency analysis and with the applications to the study of partial differential equations and signal analysis.


ERC Research Sectors:  PE1_8 Analysis, PE1_9 Operator algebras and functional analysis, PE1_11 Partial differential equations.


Research areas:

1) Microlocal Analysis

Pseudodifferential and Fourier integral operators

- Projective and Toeplitz type pseudodifferential operators

- Operator algebras

- Global wave front sets

- Microlocal analysis on manifolds

- Microlocal analysis on Gevrey classes, Gelfand-Shilov spaces, spaces of ultradistributions, L^p spaces

- Structure and decay properties of resolvents of elliptic operators

- Zeta-functions and determinants of pseudodifferential operators

- Spectral analysis for pseudodifferential operators


2) Time-frequency analysis

- Gabor frames

- Wavelet frames

- Reproducing formulae

- Time-frequency representations

- Uncertainty principles


3) Partial differential equations 

- (C^\infty, Gevrey, analytic) hypoellipticity and solvability

- Decay and regularity  of solutions to nonlinear equations

- Well-posedness of the Cauchy problem for hyperbolic systems

- Propagation of singularities

- Gabor analysis of PDE

- H_\infty-calculus and maximal L_p-regularity theory

- Boundary value problems on manifolds with geometric singularities






Prodotti della ricerca

  • 2014

U. Battisti, S. Coriasco, E. Schrohe
Fourier Integral Operators of Boutet de Monvel Type

U. Battisti, M. Borsero, S. Coriasco
Sharp Weyl Estimates for Tensor Products of Pseudodifferential Operators

M. Berra
Gabor frame decomposition of evolution operators and applications

P. Boggiatto, E. Carypis, A. Oliaro
Local uncertainty principles for the Cohen class

M. Cappiello, P. D'Ancona, F. Nicola
On the radius of spatial analyticity for semilinear symmetric hyperbolic systems

Marco Cappiello, Luigi Rodino, Joachim Toft
Radial symmetric elements and the Bargmann transform

M. Cappiello, S. Pilipovic, B. Prangoski
Parametrices and hypoellipticity for pseudodifferential operators on spaces of tempered ultradistributions

E. Carypis
Time-frequency representations in the Cohen's class and uncertainty principles

E. Cordero, F. Nicola, L. Rodino
A few remarks on time-frequency analysis of Gevrey, analytic and ultra-analytic functions

E. Cordero, J. Toft, P. Wahlberg
Sharp results for the Weyl product on modulation spaces

E. Cordero, F. Nicola
On the Schrödinger equation with potential in modulation spaces

S. Coriasco, M. Ruzhansky
Global L^p continuity of Fourier Integral Operators

S. Coriasco, M. Murdocca
L^p(R^n)-continuity of translation invariant anisotropic pseudodifferential operators: a necessary condition

S. Coriasco, K. Johansson, J. Toft
Global wave-front sets of intersection and union type

S. Coriasco, J. Toft
Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators.

S. Coriasco, K. Johansson, J. Toft
Calculus, continuity and global wave-front properties for Fourier integral operators on R^d

S. Coriasco, R. Schulz
SG-Lagrangian submanifolds and their parametrization

S. Coriasco, J. Toft
Calculus for Fourier Integral Operators in generalized SG classes

G. Garello, A. Morando
L^P microlocal properties for vector weighted pseudodifferential operators with smooth symbols

G.Garello, A. Morando
Microlocal regularity of Besov type for solutions to quasi-elliptic non linear partial differential equations

G. Garello, A. Morando
m-microlocal elliptic pseudodifferential operators acting on L^p_loc

L. Maniccia, E. Schrohe, J. Seiler
Determinants of Classical SG-pseudodifferential Operators

L.Rodino, P.Wahlberg
The Gabor wave front set

  • 2013

Globally bisingular elliptic operators

P. Boggiatto, G. De Donno, A. Oliaro
Hudson's Theorem for $\tau-$Wigner Transforms

P. Boggiatto, E. Carypis, A. Oliaro
Windowed - Wigner representations in the Cohen class and uncertainty principles

Iulia Martina Bulai, Bruna Chialva, Davide Duma, Ezio Venturino
Do niches help in controlling disease spread in ecoepidemic models?

Marco Cappiello, René Schulz
Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

E. Cordero, A. Tabacco
Triangular subgroups of Sp(d,R) and reproducing formulae

E. Cordero, F. Nicola, L. Rodino
Schrödinger equations in modulation spaces

E. Cordero, A. Tabacco, P. Wahlberg
Schrödinger type propagators, pseudodifferential operators and modulation spaces

E. Cordero, K. Gröchenig, F. Nicola, L. Rodino
Wiener Algebras of Fourier Integral Operators

S. Coriasco, L. Maniccia
On the Spectral Asymptotics of Operators on Manifolds with Ends

S. Coriasco, K. Johansson, J. Toft
Local wave-front sets of Banach and Fréchet types,and pseudo-differential operators

S. Coriasco, R. Schulz
The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions

S. Coriasco, K. Johansson, J. Toft
Global wave-front sets of Banach, Fréchet and Modulation space types, and pseudo-differential operators

G. Garello, A. Morando
Lp microlocal properties for vector weighted pseudodifferential operators with smooth symbols

G. Garello, A. Morando
L^p Microlocal properties for vector weighted pseuodifferential operators with smooth symbols

J. Seiler, A. Strohmaier
On the Noncommutative Residue for Projective Pseudodifferential Operators

 M. Fochi, G. Viola
Remarks on the conditional quadratic and the conditional d?Alembert functional equations on particular normed spaces


Ultimo aggiornamento: 23/06/2015 10:17
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