Mathematical Institute of the University of Bonn

V4B5 - Real and Harmonic Analysis

Summer term 2025

Prof. Dr. Christoph Thiele

Organisational details

• Time and place: Mo. and Th. 14-16 (c.t.) Room 0.006, Endenicher Allee 60, first lecture: Mo April 14th

• Exercises: Tu 10-12 (c.t.) Room 1.008, Endenicher Allee 60, first exercise: Tu April 15th

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

  Basis page

Overview

We will read six papers of the original literature, the list is as follows (all of them are available on arxiv as noted in addition to journal publications)

• "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.
• "Paraproducts for bilinear multipliers associated with convex sets" (O. Saari, C. T. ) arXiv:2102.10305.
• "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.
• "Bexond the scope of doubling measures: weighted martingale transforms via outer measures" (S. Treil, A. Volberg, C.T. G.) https://arxiv.org/abs/1411.5345.

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

Homework: There will be weekly homework assignments and tutorials. Students will have to obtain half of the available homework points to be admitted to the exam.

Lecture notes: It is also 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.

Examination

There will be oral exams in the week July 21- 25. A typical exam will discuss two of the papers read throughout the course, one chosen by the examiner and one by the examinee.