Mathematical Institute of the University of Bonn

V4B5 - Real and Harmonic Analysis

Winter term 2026/2027

Dr. Robert Schippa

Organisational details

• Time and place: Wed. 2 - 4 pm and Fr. 12 - 2 pm (c.t.) Room 1.006 (Zeichensaal), Physikalisches Institut Wegelerstraße, first lecture: Wed Oct 14th

• Exercises: There will be two tutorials. Time and place will be determined later.

See the syllabus for further details.

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

  Basis

Overview

The course will provide an introduction to Real and Harmonic Analysis. The topics include maximal function estimates, properties of the Fourier transform, singular integrals (Calderon-Zygmund theory, boundedness of Fourier multipliers, Littlewood-Paley theory, Bessel and Riesz potentials), and oscillatory integrals (stationary and non-stationary phase, Strichartz estimates). Further topics include pseudo-differential operators (symbolic calculus, L^p-boundedness) and Fourier series (pointwise convergence). Finally, we aim for an introduction to more recent developments in Fourier restriction theory: multilinear Fourier restriction, decoupling, and applications.

Prerequisites: Basic Bachelor level courses in Analysis: measure and integration theory, and basic functional analysis.

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: References for the lecture are Stein: "Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals" and Grafakos: "Classical Fourier analysis". For the more specialized topics, we will lean on research papers as well.

Examination

Depending on the number of registrations, there will either be oral exams or a written exam. The examination periods are to be determined (presumably beginning - mid February, and midMarch 2027).