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Next: 2.3. Non-linear Partial Differential Up: Analysis Previous: 2.1. Operator Theory and

2.2. Lie Groups, Special Functions, Approximation Theory and Complex Analysis

Programme leaders: G. van Dijk, T.H. Koornwinder

Central research themes are:
(1) analysis on Lie groups, semisimple symmetric spaces and quantum groups

(2) special functions associated with root systems and their interpretation on the above-mentioned structures

(3) analysis, asymptotics, approximation theoretic properties and algorithmic aspects of special functions and orthogonal polynomials in one variable (including the cases of orthogonal rational functions and orthogonality in a Sobolev space)

(4) approximation problems with relation to potential theory

(5) analysis in several complex variables.

This programme unites a number of themes which are mutually connected and have a stimulating influence on each other. Some themes have a quite algebraic setting, while others belong to calssical analysis. Theme (2) dealing with Heckman-Opdam hypergeometric functions and q-analogues like Macdonald polynomials is a highlight of the programme. A new line within theme (1) is the study of canonical representations for Hermitian and para-Hermitian symmetric spaces, and its relation with Berezin quantization.

Fri Mar 20 16:01:06 MET 1998