Mathematical Institute of the University of Bonn

V4B5 - Real and Harmonic Analysis

Summer term 2025

Dr. Michel Alexis, Prof. Dr. Asgar Jamneshan

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 and Th 16-18 (c.t.) Room 1.008, Endenicher Allee 60, first exercise: Tu April 15th

See the syllabus for further details.

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

  Basis page

Overview

In this course, we will cover several classical topics, including the Hardy Littlewood maximal function, Calderon-Zygmund theory, Singular integrals, stationary phase, multiplier theory, Littlewood-Paley theory and pointwise convergence of Fourier series. If time permits, we will cover additional topics, which may include time frequency analysis and weighted norm inequalities.

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.

Course text: Our main text of reference will be "Classical and Multilinear Harmonic Analysis" by Muscalu-Schlag. We will however supplement with other resources, such as "Classical Fourier Analysis" by Grafakos, "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" by Stein, and other resources. We will also lean on some research papers for the additional topics.

Examination

There will be oral exams in the week July 28-August 1.