Course Syllabus for

Riesz Products and Applications
Rieszprodukter med tillämpningar

FMA300F, 5 credits

Valid from: Spring 2015
Decided by: FN1/Anders Gustafsson
Date of establishment: 2015-04-18

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English


To make the participants acquainted with the theory of Riesz products which constitute a usefool tool for research in mathematical analysis. Among other things they have been used to give examples of continuous, nowhere differentiable functions and of periodic functions, the Fourier coefficients of which decay as slowly as for typical piecewise continuous functions with discontinuities.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must Be able to use Riesz products to construct functions with desired “exotic” properties.

Course Contents

Construction of Riesz products on different groups (in particular S^1); Basic properties; Random Riesz products; Almost everywhere convergence of lacunary Fourier series; Applications to Diophantine approximation and multifractal analysis of some ergodic averages.

Course Literature

Lecture notes will be provided.

Instruction Details

Type of instruction: Lectures

Examination Details

Examination formats: Written exam, oral exam. Take-home exam
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: Integration Theory, Fourier Analysis, Nonlinear Dynamic Systems

Course Occasion Information

Contact and Other Information

Course coordinators:

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