Universität Wien
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510004 SE Harmonic Analysis (VSM) (2025S)

4.00 ECTS (2.00 SWS), SPL 51 - Doktoratsstudium Mathematik
Continuous assessment of course work
Moodle

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

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 04.03. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 11.03. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 18.03. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 25.03. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 01.04. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 08.04. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 29.04. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 06.05. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 13.05. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 20.05. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 27.05. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 03.06. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 10.06. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 17.06. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01
  • Tuesday 24.06. 11:30 - 13:00 Seminarraum 9, Kolingasse 14-16, OG01

Information

Aims, contents and method of the course

The goal of this seminar is to discuss various results on norms of linear combinations of complex exponentials. This allows the participants to build up a working knowledge for research in Fourier analysis.

Parseval’s identity from Fourier analysis asserts that the 2-norm of a linear combination of complex exponentials with integer frequencies (Fourier series) is equal to the 2-norm of the coefficients. The first aim of the seminar is to obtain similar inequalities for complex exponentials with possibly noninteger frequencies (nonharmonic Fourier series), namely inequalities relating the 2-norm of a nonharmonic Fourier series and its coefficients. The central result for such nonharmonic Fourier series is Ingham’s theorem. After studying 2-norms of nonharmonic Fourier series, we will continue with studying estimates for their 1-norms, where new phenomena occur. Among the results that will be discussed are Littlewood’s conjecture for harmonic Fourier series and Nazarov’s inequality for nonharmonic Fourier series.

The format of the seminar is that of a reading seminar based on the paper “From Ingham to Nazarov’s inequality: a survey on some trigonometric inequalities” by P. Jaming and C. Saba.

Active participation and seminar presentation is required

Assessment and permitted materials

To obtain a grade, participants should attend the seminar regularly and give a presentation on a suitable topic in harmonic analysis.

Minimum requirements and assessment criteria

Active participation and seminar presentation. Assistance is mandatory. Students cannot miss more than two appointments, and these absences need to be excused in advance (e.g., by email to the teacher).

Examination topics

Topics related to the presentations.

Reading list

P. Jaming, C. Saba. From Ingham to Nazarov’s inequality: a survey on some trigonometric inequalities. Adv. Pure Appl. Math. 15, No. 3, 12-76 (2024).

Association in the course directory

MAMS;MANS

Last modified: Tu 25.02.2025 16:47