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Seminar/Proseminar: Spaces of Holomorphic Functions
Organization
There will be a kick-off meeting on the 9th of February at 14:00 in SR 6. In this meeting, detailed information regarding this seminar will be shared, and you will have the opportunity to ask questions. If you can't attend the kick-off meeting or if you already have questions concerning this seminar, you may contact Maximilian Leist.
Time and Place
The seminar's timeslot will be determined in the kick-off meeting, depending on the audience's preferences.
Content
At the intersection of complex analysis and functional analysis, Hilbert and Banach spaces of holomorphic functions play an important role. These spaces enable the study of functional-analytic problems using methods from complex analysis and vice versa, contributing to a fruitful interplay between these two fields. The goal of this seminar is to study operator theoretic as well as function theoretic aspects of such spaces. The spaces that we will mainly focus on are Hardy and Bergman spaces, as well as the Dirichlet space.
A list of possible talk topics can be found here (link).
Prerequisites
- Basic knowledge of real analysis, linear algebra and Lebesgue integration (e.g. Analysis 1-3 and Lineare Algebra 1-2 at UdS).
- Complex analysis (e.g. Funktionentheorie at UdS).
- While many talks will only require basic definitions in functional analysis (e.g. Banach and Hilbert spaces), deeper knowledge of the subject (e.g. the contents of Functional Analysis 1 at UdS) is highly recommended, but not mandatory.
Mode
This course can either be taken as a seminar or as a proseminar. Depending on your choice, you are expected to fulfill the following requirements:
- Proseminar: Give a talk of approximately 80 minutes on a selected topic, be regularly present in class.
- Seminar: Give a talk of approximately 80 minutes on a selected topic, be regularly present in class, write a report of 10-15 pages that covers your talk topic and may go beyond that.