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Analisi microlocale e tempo-frequenza

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Attività

 

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

 

 

 

 

 


 

 

 

2013

Prof. E. Schrohe (Leibniz Universität Hannover), Gennaio-Marzo 2013 (due settimane in totale)

Prof. J. Toft (Linnaeus University, Växjö), Febbraio 2013 (una settimana) e Dicembre 2013 (una settimana)

Prof. N. Teovanov, Prof. S. Pilipovic (Università di Novi Sad), Marzo 2013 (una settimana)

Visiting Professors (2011-13)

2011

Prof. T. Gramchev (Cagliari) and Prof. A. Kirillov (Brasil), January 20-22
Prof. F. Fathizadeh (USA), June 27-30

2012

Prof. E. Schrohe, Prof. J. Escher (Leibniz Universität Hannover), January (1 week)

Prof. J.Carlovich (Mexico), May 27-30
Dr. R.Schulz (Germany), July (1 month)
Prof. P.Popivanov (Bulgaria), August 26-30
Prof. Okada (Japan), September 12-14

2013

Prof. E. Schrohe (Leibniz Universität Hannover), January-March (2 weeks)

Prof. J. Toft (Linnaeus University, Växjö), February (1 week) and December  (1 week)

Prof. N. Teovanov, Prof. S. Pilipovic (University of Novi Sad), March 2013 (1 week)

Prof.  M.W. Wong (Canada), Aprile 1-5.

 

Visits abroad (2011-13) (one month or more)

- Georgia Institute of Technology, Atlanta (E. Carypis, June-December 2012, 6 months)

 - Institut für Analysis, Gotfried Wilhelm Leibniz Universität Hannover (S. Coriasco, November 2011- February 2012, 3 months)

- Department of Mathematics, University of Novi Sad (S. Coriasco, March 2012, 1 month)

- Department of Mathematics, Linnaeus Universität, Växjö (S. Coriasco, May-June 2012, 6 weeks)

 

Collaborations with foreign institutions 

Gotfried Wilhelm Leibniz Universität Hannover (Germany)

Linnaeus University of Vaxjo (Sweden)

Imperial College of London (UK)

University of Novi Sad (Serbia)

Purdue University (USA)

University of Vienna (Austria)

Universitat Politecnica de Valencia (Spain)

York University of Toronto (Canada)

University of Sofia (Bulgaria)

 

Weekly seminar

Analysis Seminars - Seminari di Analisi Matematica

http://webmath2.unito.it/seminarianalisi/

In collaboration with the Nonlinear Differential Equations Group (organizers: Vivina Barutello, Sandro Coriasco)

 

Research grants

- Prin 2012 research project "Variational and perturbative aspects of nonlinear differential problems" (2014-17) supported by the Italian Ministry of Research as a Project of National Interest (Participants: M. Cappiello, S. Coriasco, E. Cordero, J. Seiler).

Advanced courses

- "Introduction to Gabor Analysis I and II" (A. Oliaro, P. Boggiatto) AA 2010-11,

http://dott-matematica.campusnet.unito.it/do/corsi.pl/Show?_id=221a;sort=DEFAULT;search=%20{aa}%20%3d~%20m%2f2010%2fi%20and%20{aa}%20%3d~%20m%2f2011%2fi%20;hits=11 

-  "Pseudo-differential operators and time-frequency analysis"  (E. Cordero, J. Seiler) AA 2011-12,  
http://dott-matematica.campusnet.unito.it/do/corsi.pl/Show?_id=e3c7

- "Introduction to the calculus of pseudodifferential and Fourier integral operators'' (S. Coriasco) AA 2011-12 (University of Novi Sad).

- "Applications of Fourier analysis" (E. Cordero, J. Seiler) AA 2012-13,

http://dott-matematica.campusnet.unito.it/do/corsi.pl/Show?_id=3173;sort=DEFAULT;search=%20{aa}%20%3d~%20m%2f2012%2fi%20and%20{aa}%20%3d~%20m%2f2013%2fi%20;hits=16

- Reading course "Cauchy problems for covariant equations" (S. Coriasco, in collaboration with L. Fatibene) AA 2012-13

http://dott-matematica.campusnet.unito.it/do/corsi.pl 

 

 Invited talks

Ubertino Battisti

- Lecture at the "Workshop on Elliptic and Parabolic Equations", Hannover, Spetember 10-12.

Michele Berra

- Lecture at XXXIII Convegno Nazionale di Analisi Armonica, Alba, June 17-20.

Marco Cappiello

- Seminar at the University of Novi Sad, April 15.

Evanthia Carypis

- Lecture at the International Symposium Italia Serbia "Pseudodifferential operators and microlocal analysis", University of Torino, March 13, 2013.

- Lecture at GPOTS 2013, University of California, Berkeley, May .

Elena Cordero

- Lecture at XXXIII Convegno Nazionale di Analisi Armonica, Alba, June 17-20.

Sandro Coriasco

- Lecture at the International Symposium Italia Serbia "Pseudodifferential operators and microlocal analysis", University of Torino, March 13, 2013.

Luigi Rodino

- Seminar at the University of Novi Sad, December.

Joerg Seiler

 - Seminar at the University of Regensburg, October.

Massimo Borsero

- Lecture at the workshop "Geometric and Singular Analysis'', Potsdam March 25-29.

- Lecture at the International Symposium Italia Serbia "Pseudodifferential operators and microlocal analysis", University of Torino, March 13, 2013.

 

 

 Visiting professors

- Prof. E. Schrohe, Gottfried Wilhelm Leibniz Universität Hannover, January 13-17.
- Prof. C. Fernandez and Prof. A. Galbis, January 20-30.
- Prof. M. Reissig, TU Bergakademie Freiberg, Germany, November 2-8.
- Prof. B.-W. Schulze, University of Potsdam, Germany.
- Prof. V. Turunen, Aalto University, Finland, December.
- Prof. P. Wahlberg (Linnaeus University, Växjö, Sweden.
- Prof. J. Toft, University of Växjö, Sweden, November 23-29.
- Dr. U. Kiran, Sri Sathya Sai Institute of higher learning, India, May 1-June 30 (2 months).

 

Visits abroad (one month or more)

Purdue University (M. Berra, January 6 - February 14).

University of Vienna (NuHAG group) (I.M. Bulai, February 1- March 31).

 

Collaborations with foreign institutions 

Gotfried Wilhelm Leibniz Universität Hannover (Germany)

Linnaeus University of Vaxjo (Sweden)

Imperial College of London (UK)

University of Novi Sad (Serbia)

Purdue University (USA)

University of Vienna (Austria)

Universitat de Valencia (Spain)

York University of Toronto (Canada)

Sri Sathya Sai Institute of Higher Learning (India)

 

Weekly seminar

Analysis Seminars - Seminari di Analisi Matematica

http://webmath2.unito.it/seminarianalisi/

In collaboration with the Nonlinear Differential Equations Group (organizers: Vivina Barutello, Sandro Coriasco)

 

Research grants

- Prin 2012 research project "Variational and perturbative aspects of nonlinear differential problems" (2014-17) supported by the Italian Ministry of Research as a Project of National Interest (Participants: M. Cappiello, S. Coriasco, E. Cordero, J. Seiler).

- GNAMPA 2014 project "Time-frequency analysis and applications" (PI: U. Battisti, participants: M. Berra, I. Bulai, E. Carypis, E. Cordero, L. Rodino, A. Oliaro).

- GNAMPA 2014 project "Evolution and stochastic partial differential equations" (PI: S. Coriasco, participants: M. Borsero, M. Cappiello).

Advanced courses

- Analysis on Manifolds (DM 270)
 

- Harmonic and Fourier analysis (DM 270)

http://matematicalm.campusnet.unito.it/do/corsi.pl/Show?_id=nnqs;sort=DEFAULT;search=;hits=225

 

Invited talks (2014)

Ubertino Battisti

- Lecture at the workshop "Geometric and singular analysis", Potsdam (Germany), March 23-28.

- Lecture at the Conference "Modern Time-Frequency Analysis", Strobl (Austria), June 1-6.

-Seminar at the Institut für Analysis, Gottfried Wilhelm Leibniz Universität Hannover (Germany), June 25.

Michele Berra

- Lecture at the annual project review meeting, Chicago, April 30 - May 2.

- Lecture at the Conference "Modern Time-Frequency Analysis", Strobl (Austria), June 1-6.

Marco Cappiello

- Lecture at the workshop "Geometric and singular analysis", Potsdam (Germany), March 23-28.
- Lecture at the II International Workshop "Global Properties of PDEs on Manifolds", Cagliari, September 17-19.

Sandro Coriasco

- Seminar at the Linnaeus Universität, Växjö (Sweden), March 6.
- Lecture at the workshop "Geometric and Singular Analysis", Potsdam (Germany), March 24-28.
- Seminar at the Institut für Analysis, Gottfried Wilhelm Leibninz Universität Hannover (Germany), June 3.
- Lecture at the Conference "Days of Analysis in Novi Sad 2014 - DANS14", Novi Sad (Serbia) July 3-7.
- Lecture at the International Conference "Generalized Function 2014", Southampton (UK), September 8-12.

Alessandro Oliaro

- Lecture at the First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Bilbao (Spain), June 30, July 4.
- Seminar at the University of Ferrara, November 24.

Luigi Rodino


- Lecture at the Conference "Modern Time-Frequency Analysis", Strobl (Austria), June 1-6.
- Lecture at the Conference "Days of Analysis in Novi Sad 2014 - DANS14", Novi Sad (Serbia) July 3-7.
- Lecture at the International Conference "Generalized Function 2014", Southampton (UK), September 8-12.

 

 

 

Prodotti della ricerca

U. Battisti, S. Coriasco, E. Schrohe
Fourier Integral Operators of Boutet de Monvel Type
http://hdl.handle.net/2318/151593

U. Battisti, M. Borsero, S. Coriasco
Sharp Weyl Estimates for Tensor Products of Pseudodifferential Operators
http://hdl.handle.net/2318/151604

M. Berra
Gabor frame decomposition of evolution operators and applications
http://hdl.handle.net/2318/143236

P. Boggiatto, E. Carypis, A. Oliaro
Local uncertainty principles for the Cohen class
http://hdl.handle.net/2318/149791

M. Cappiello, P. D'Ancona, F. Nicola
On the radius of spatial analyticity for semilinear symmetric hyperbolic systems
http://hdl.handle.net/2318/142296

Marco Cappiello, Luigi Rodino, Joachim Toft
Radial symmetric elements and the Bargmann transform
http://hdl.handle.net/2318/149030

M. Cappiello, S. Pilipovic, B. Prangoski
Parametrices and hypoellipticity for pseudodifferential operators on spaces of tempered ultradistributions
http://hdl.handle.net/2318/151569

E. Carypis
Time-frequency representations in the Cohen's class and uncertainty principles
http://hdl.handle.net/2318/142417

E. Cordero, F. Nicola, L. Rodino
A few remarks on time-frequency analysis of Gevrey, analytic and ultra-analytic functions
http://hdl.handle.net/2318/143493

E. Cordero, J. Toft, P. Wahlberg
Sharp results for the Weyl product on modulation spaces
http://hdl.handle.net/2318/151504

E. Cordero, F. Nicola
On the Schrödinger equation with potential in modulation spaces
http://hdl.handle.net/2318/151522

S. Coriasco, M. Ruzhansky
Global L^p continuity of Fourier Integral Operators
http://hdl.handle.net/2318/47272

S. Coriasco, M. Murdocca
L^p(R^n)-continuity of translation invariant anisotropic pseudodifferential operators: a necessary condition
http://hdl.handle.net/2318/129968

S. Coriasco, K. Johansson, J. Toft
Global wave-front sets of intersection and union type
http://hdl.handle.net/2318/151599

S. Coriasco, J. Toft
Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators.
http://hdl.handle.net/2318/151600

S. Coriasco, K. Johansson, J. Toft
Calculus, continuity and global wave-front properties for Fourier integral operators on R^d
http://hdl.handle.net/2318/151601

S. Coriasco, R. Schulz
SG-Lagrangian submanifolds and their parametrization
http://hdl.handle.net/2318/151602

S. Coriasco, J. Toft
Calculus for Fourier Integral Operators in generalized SG classes
http://hdl.handle.net/2318/151605

G. Garello, A. Morando
L^P microlocal properties for vector weighted pseudodifferential operators with smooth symbols
http://hdl.handle.net/2318/134129

G.Garello, A. Morando
Microlocal regularity of Besov type for solutions to quasi-elliptic non linear partial differential equations
http://hdl.handle.net/2318/151263

G. Garello, A. Morando
m-microlocal elliptic pseudodifferential operators acting on L^p_loc
http://hdl.handle.net/2318/151264

L. Maniccia, E. Schrohe, J. Seiler
Determinants of Classical SG-pseudodifferential Operators
http://hdl.handle.net/2318/143877

L.Rodino, P.Wahlberg
The Gabor wave front set
http://hdl.handle.net/2318/143487

U.Battisti,T.Gramchev,S.Pilipovic,L.Rodino
Globally bisingular elliptic operators
http://hdl.handle.net/2318/128459

P. Boggiatto, G. De Donno, A. Oliaro
Hudson's Theorem for $\tau-$Wigner Transforms
http://hdl.handle.net/2318/132773

P. Boggiatto, E. Carypis, A. Oliaro
Windowed - Wigner representations in the Cohen class and uncertainty principles
http://hdl.handle.net/2318/98287

Iulia Martina Bulai, Bruna Chialva, Davide Duma, Ezio Venturino
Do niches help in controlling disease spread in ecoepidemic models?
http://hdl.handle.net/2318/145493

Marco Cappiello, René Schulz
Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions
http://hdl.handle.net/2318/151443

E. Cordero, A. Tabacco
Triangular subgroups of Sp(d,R) and reproducing formulae
http://hdl.handle.net/2318/128121

E. Cordero, F. Nicola, L. Rodino
Schrödinger equations in modulation spaces
http://hdl.handle.net/2318/132052

E. Cordero, A. Tabacco, P. Wahlberg
Schrödinger type propagators, pseudodifferential operators and modulation spaces
http://hdl.handle.net/2318/141881

E. Cordero, K. Gröchenig, F. Nicola, L. Rodino
Wiener Algebras of Fourier Integral Operators
http://hdl.handle.net/2318/130438

S. Coriasco, L. Maniccia
On the Spectral Asymptotics of Operators on Manifolds with Ends
http://hdl.handle.net/2318/129967

S. Coriasco, K. Johansson, J. Toft
Local wave-front sets of Banach and Fréchet types,and pseudo-differential operators
http://hdl.handle.net/2318/100146

S. Coriasco, R. Schulz
The global wave front set of tempered oscillatory integrals with inhomogeneous phase functions
http://hdl.handle.net/2318/127348

S. Coriasco, K. Johansson, J. Toft
Global wave-front sets of Banach, Fréchet and Modulation space types, and pseudo-differential operators
http://hdl.handle.net/2318/70065

G. Garello, A. Morando
Lp microlocal properties for vector weighted pseudodifferential operators with smooth symbols
http://hdl.handle.net/2318/151610

G. Garello, A. Morando
L^p Microlocal properties for vector weighted pseuodifferential operators with smooth symbols
http://hdl.handle.net/2318/151262

J. Seiler, A. Strohmaier
On the Noncommutative Residue for Projective Pseudodifferential Operators
http://hdl.handle.net/2318/136717

 M. Fochi, G. Viola
Remarks on the conditional quadratic and the conditional d?Alembert functional equations on particular normed spaces
http://hdl.handle.net/2318/128369

 

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