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Spectral theory of rank one dynamical systems
El Houcein El Abdalaoui (LMRS, l'Universit de Rouen, France) e

PROGRAM OF THE COURSE
Part I: Riesz products via harmonic analysis.

In this part we discuss dierent classes of probability measures on R constructed with the help of Riesz products, including Salem question. a) Zygmund singularity criterion. b) Theorem on mutual singularity due to Peyriere.
Part II: Generalized Riesz products as spectral types of dynamical systems (Z-actions).

1) Ledrappier example (classical Riesz products). 2) Spectral type of the Morse substitution. 3) On the spectral type of subsitutions with (multi-dimensional Riesz products) with applications to interval exchange transformations. 4) HostParreauM theorem. ela 5) Spectral type of a rank one transformation via Bourgain technique. 6) Bourgain singularity criterion. 7) Conditions for existence of the Lebesgue component. 8) Bourgain and KlemesReinhold theorems on spectral type of a rank one transformation.
Part III: Generalized Riesz products as spectral types of dynamical systemes (countable group actions).

9) Examples due to Ismagilov. 10) HelsonParry and Guenais exemples.
Course wil l be held at IUM MCCME, starting from February 27, 2012