PhD in Pure and Applied Mathematics

The aim of this course is to introduce the audience to modern techniques in harmonic analysis with a special emphasis on the underlying symplectic symmetries; open problems will be discussed. We will give applications to time-frequency analysis and to mathematical quantization problems. A few topics we will address are the following:

• Preliminaries on time-frequency analysis and related function spaces

• The metaplectic representation of the symplectic group;

• Maslov and Conley-Zehnder indices, applications to symplectic and metaplectic isotopies;

• Weyl pseudodifferential calculus and the Wigner formalism;

• Positivity properties of trace class operators;

• Born-Jordan pseudodifferential operators; open problems.

 

Maurice A. de Gosson, Symplectic Methods in Harmonic Analysis and in Mathematical Physics, volume 7 of Pseudo-Differential Operators. Theory and Applications, Birkhäuser/Springer Basel, 2011

Maurice A. de Gosson, Born-Jordan quantization, Fundamental Theories of Physics, 182, Theory and applications, Springer, 2016

 

Karlheinz Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser Boston, 2001

Durata: 20 ore frontali, seminari di approfondimento tenuti dagli studenti 

Periodo del corso: Gennaio-Marzo 2018

 

Le lezioni del Prof. de Gosson si terranno in aula Lagrange, nel seguente orario:

 

Mon 22/1/2018:  10-12

Tue 23/1/2018: 11:30-13:30

Wed 24/1/2018: 14-16

Thu 25/1/2018: 10-12

Fri 26/1/2018: 11:30-13:30