Tuesday, 9:00 - 11:00, ESI, Schrödinger lecture hall
2nd part March 6 - April 24, 2007

 
The course will cover analysis on bounded symmetric domains in Cⁿ and related topics and applications from operator theory, several complex variables, harmonic analysis, and mathematical physics. Participants are expected to have some training in functional analysis and Fourier theory.

The lecture will consist of two parts. The first part, to be delivered in January 2007, will be of introductory nature, concentrating on the prerequisites from several complex variables, reproducing kernel Hilbert spaces, and group representations. The second part will resume in the beginning of March and continue to the end of April, and will discuss harmonic analysis on bounded symmetric domains, the various associated spaces of holomorphic functions, operators acting on these (invariant differential, Toeplitz, Hankel, localization, etc.), and applications of all these in mathematical physics etc. In particular, we will treat such current topics as the recent generalizations of the Weyl calculus by Arazy and Upmeier, Arveson's theory of coanalytic models, Berezin's quantization and its ramifications, or the bilinear invariant operators (transvectants) of Peetre, Janson, Rochberg and Zhang. Finally, we also briefly indicate to what extent can all this be extended beyond the symmetric setting, i.e. to general pseudoconvex domains in Cⁿ.