Details for the Course Syllabus for Course FMA300F valid from Spring 2015

General

Aim

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.

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.

Knowledge and Understanding

For a passing grade the doctoral student must
be able to account for the construction of Riesz products.
Be able to give examples of applications to the theory of dynamical systems.

Competences and Skills

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

Judgement and Approach

Types of Instruction

Examination Formats

Admission Requirements

Assumed Prior Knowledge

Selection Criteria

Literature

Further Information

Course code

Administrative Information

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