V5B8 - Selected Topics in Analysis -Topis in Euclidean Harmonic Analysis

Summer term 2024

Prof. Dr. Christoph Thiele

Organisational details

• Time and place: Thu 14-16 (c.t.), Room N0.008, Endenicher Allee 60 (Annex), first lecture: Thu April 11th
• UPDATE: DUE TO HOLIDAYS MAY 9 AND MAY 30, WE HAVE LECTURES TUESDAYS MAY 7 AND MAY 28 FROM 6(ct)-8 PM IN ROOM 00.11. Inbetween these two tuesdays, there is no lecture due to me being out of town one week and pentecost break the other week.

• If you are a participating Masters student, please register on Basis.

  Basis page

Overview

We will read four papers of the original literature, the list is as follows

• "When does exp(-tau) maximize Fourier extension for a conic section?" (G. Negro, D. Oliveira e Silva, C.T.) arXiv:2209.03916. We read the proof of Foschi's theorem in Section 2.
• "The Hilbert transform does not map L1(Mw) to L1,infty(w)" (M. Reguera, C.T.) arXiv:1011.1767.
• "An L4 estimate for a singular entangled quadrilinear form" (P. Durcik) arXiv:1412.2384.
• "Quantum signal processing and nonlinear Fourier analysis" (M. Alexis, G. Mnatsakanyan, C.T.) https://arxiv.org/abs/2310.12683.

Prerequisites: Basic Bachelor level courses in Analysis. In particular familiarity with Fourier analysis and Lebesgue measure theory is helpful.

Homework: It is expected that students read and work through and understand the discussed papers (in so far as discussed in the course) as well as the important references therein, concurrently with the lectures.

Lecture notes: Matthias Mayer has taken fotos of the black boards and kindly shares under the following:

link

Examination