Engelska

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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.

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.

be able to account for the construction of Riesz products.
Be able to give examples of applications to the theory of dynamical systems.

Be able to use Riesz products to construct functions with desired “exotic” properties.

Föreläsningar

Skriftlig tentamen

Muntlig tentamen

Take-home exam

Underkänd, godkänd

Integration Theory, Fourier Analysis, Nonlinear Dynamic Systems

 

Lecture notes will be provided.

FMA300F

 -04-18

FN1/Anders Gustafsson