Курс:Спектральная теория систем ранга один

Материал из TDS

Версия 15:29, 27 января 2012

Лектор - профессор El Houcein El Abdalaoui, Laboratoire de Mathématiques Raphaël Salem (LMRS), l'Université de Rouen

Курс читается на английском языке.

Организаторы: Кафедра теории динамических систем / МИАН / Русско-французская лаборатория Poncelet / МЦНМО

ПРОГРАММА КУРСА

Part I: Riesz products via harmonic analysis

In this part we discuss different 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 Peyrière

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. Host-Parreau-Méla theorem.
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 Klemes-Reinhold 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. Helson-Parry and Guenais exemples.

Курс читаться в МНУ МЦНМО. Первая лекция - 27 февраля 2012