Universität Wien

510004 SE Harmonic Analysis (VSM) (2025S)

4.00 ECTS (2.00 SWS), SPL 51 - Doktoratsstudium Mathematik
Prüfungsimmanente Lehrveranstaltung
Moodle
Di 24.06. 11:30-13:00 Seminarraum 9, Kolingasse 14-16, OG01

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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

Art der Leistungskontrolle und erlaubte Hilfsmittel

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

Mindestanforderungen und Beurteilungsmaßstab

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).

Prüfungsstoff

Topics related to the presentations.

Literatur

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).

Zuordnung im Vorlesungsverzeichnis

MAMS;MANS

Letzte Änderung: Di 25.02.2025 16:47