Universität Wien FIND

Return to Vienna for the summer semester of 2022. We are planning to hold courses mainly on site to enable the personal exchange between you, your teachers and fellow students. We have labelled digital and mixed courses in u:find accordingly.

Due to COVID-19, there might be changes at short notice (e.g. individual classes in a digital format). Obtain information about the current status on u:find and check your e-mails regularly.

Please read the information on https://studieren.univie.ac.at/en/info.

250046 VO Topics in Analysis (2018W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Monday 01.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 02.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 08.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 09.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 15.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 16.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 22.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 23.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 29.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 30.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 05.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 06.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 12.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 13.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 19.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 20.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 26.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 27.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 03.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 04.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 11.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 08.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 14.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 15.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 21.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 22.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Monday 28.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 29.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

A first goal of the course is to study classical spaces of analytic functions on the plane (Fock 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.

Second, Fock spaces will be described in terms of the representation theory of the Heisenberg group. Sampling and interpolation theorems will be recast in terms of coherent systems for the Heisenberg group. As an application, the spanning properties of families of modulations and translations of the Gaussian will be completely described.

Third, more general tools to study sampling and interpolation problems in contexts without analyticity will be introduced. Concrete examples will be discussed.

Prerequisites: basic complex, functional, and Fourier analysis.

See also:

https://sites.google.com/site/jlromeroresearch/teaching

Assessment and permitted materials

Oral exam

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

* Kristian Seip, Interpolation and Sampling in Spaces of Analytic Functions, University Lecture Series 33. Providence, RI: American Mathematical Society (AMS). xii, 139 p., (2004)

* Peter Duren and Alexander Schuster, Bergman Spaces
American Mathematical Society (AMS), Mathematical Surveys and Monographs, Vol.100 (2004).

* Haakan Hedenmalm, B. Korenblum and Kehe Zhu, Theory of Bergman Spaces. Springer, (2000).

* Gerald B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, (1989).

* Specialized references / lecture notes will be provided during the course.

Association in the course directory

MANV

Last modified: Mo 07.09.2020 15:40