Valid from: Spring 2015
Decided by: FN1/Anders Gustafsson
Date of establishment: 2015-04-18
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.
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.
Lecture notes will be provided.
Type of instruction: Lectures
Examination formats: Written exam, oral exam.
Grading scale: Failed, pass
Assumed prior knowledge: Integration Theory, Fourier Analysis, Nonlinear Dynamic Systems