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250089 VO Topics in Harmonic Analysis (2021W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
ON-SITE

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Thursday 07.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 14.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 21.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.10. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 28.10. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 04.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 11.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 18.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.11. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 25.11. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.12. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 02.12. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 09.12. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.12. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 16.12. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.01. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 13.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.01. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 20.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.01. 15:00 - 16:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 27.01. 11:30 - 13:00 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The goal of the course is to study classical spaces of analytic functions on the unit disk (Bergman spaces) and the problems of sampling (recovering a function from its values on a certain set) and interpolation (prescribing the values of a function on a given set). Both problems admit a complete geometric solution in terms of certain densities, and this will be presented in detail.
Applications to signal analysis will be developed.

The required background on complex analysis will also be provided during the course and it may be of independent interest (e.g., relation between the growth of an analytic function and the density of its zero set, factorization theorems).

Assessment and permitted materials

Oral exam / presentation of a topic for the class.

Minimum requirements and assessment criteria

Understanding of the topics. Ability to present the main results orally.

Examination topics

Topics covered during the course

Reading list

* Haakan Hedenmalm, B. Korenblum and Kehe Zhu, Theory of Bergman Spaces. Springer, (2000).
* Peter Duren and Alexander Schuster, Bergman Spaces, American Mathematical Society (AMS), Mathematical Surveys and Monographs, Vol.100 (2004).
* Kristian Seip, Interpolation and Sampling in Spaces of Analytic Functions, University Lecture Series 33. Providence, RI: American Mathematical Society (AMS). xii, 139 p., (2004)
* Kristian Seip, Regular sets of sampling and interpolation for weighted Bergman spaces. Proc. Amer. Math. Soc. 117 (1993), no. 1, 213–220.
* Kristian Seip, Beurling type density theorems in the unit disk. Invent. Math. 113 (1993), no. 1, 21–39.

Association in the course directory

MANV; MAMV

Last modified: Th 16.09.2021 10:09