19th European Intensive Course

on Complex Analysis, its Generalizations and Applications


The 19th European Intensive Course, March 17-28, 2014, to be held at the University of Aveiro, will have a total of 18 hours of lecture time, at postgraduate level, introducing topics of high current interest. This year the Intensive Course will be centered around the following topics:

Inverse Problems, Harmonic Analysis, and Representation Theory

During the course there will be extended coffee breaks in a relaxed environment where lecturers and participants are encouraged to share ideas in a more informal way. Successfully participating students will get a certificate.

Intertwining the two weeks of the course, we announce the 16th Annual Workshop on Applications and Generalizations of Complex Analysis, to be held on March 21-22, 2014.

POSTER of the 19th EIC

LECTURERS - Tentative schedule, titles & abstracts

Lecture Room - Sala Sousa Pinto (room equipped with beamer and white board)

1st week, March 17-20

Jens Wirth, Universität Stuttgart, Germany

A Rough Guide to Non-Commutative Phase Space

We present a rough guide to operator theory on compact Lie groups and associated global symbolic calculi. The course will be organised as follows:

(1) Basics:

  1. Peter--Weyl theorem and (noncommutative) Fourier transform on compact Lie groups.

  2. Examples: Tori and S^3.

  3. Function spaces and their Fourier characterisation.

  4. Schwartz kernels of operators, right-convolution kernels.

(2) Differential operators and difference operators

  1. (Left-) Invariant differential operators and their symbols.

  2. What are difference operators acting on symbols?

  3. Calculus rules for difference operators.

  4. Taylor expansions and admissibility.

(3) Functional calculus of left-invariant operators

  1. Analytic functional calculus for matrices. 

  2. Key lemmata.

  3. Bounded symbols and operators, unbounded operators.

(4) Symbol classes and pseudo-differential operators

  1. Symbol classes and asymptotic expansions.

  2. Basic calculus statements.

  3. Ellipticity.

  4. Boundedness.

  5. Functional calculus.

  6. Operator classes characterised by symbols.

It will be assumed that participants have basic knowledge in contemporary analysis, in particular concerning distribution theory, trigonometric series and the analysis of differential operators.


2nd week, March 24-28

Frank Sommen, Ghent University, Belgium

Introduction to Clifford Analysis 

Lectures notes: pdf1  pdf2

Daniel Alpay, Ben-Gurion University of the Negev, Israel   

Infinite dimensional analysis, non commutative stochastic distributions and applications

Lectures notes: pdf

Lecture 1:  Countably normed spaces, their duals and Gelfand triples

Lecture 2:  Positive definite functions, Bochner and Bochner-Minlos theorem. Hida's white noise space and Kondratiev's spaces of stochastic distributions

Lecture 3: Stationary increments stochastic processes. Linear stochastic systems.

Lecture 4: Fock spaces and non commutative stochastic distributions

Lecture 5: The free setting. Free (non commutative) stochastic processes.

Lecture 6: A new class of topological algebras


Uwe Kaehler                   
Paula Cerejeiras

Departamento de Matemática, Universidade de Aveiro                   
Campus de Santiago
P-3810-193 Aveiro 

fax: +351-234370066                                    tel: +351-234370359                                  e-mails: ukaehler@ua.pt   pceres@ua.pt

These events are supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project PEst-OE/MAT/UI4106/2014.