Курс:Спектральная теория систем ранга один

Лектор - профессор [http://www.univ-rouen.fr/LMRS/Persopage/Elabdalaoui/ El Houcein El Abdalaoui], [http://www.univ-rouen.fr/LMRS/ Laboratoire de Mathématiques Raphaël Salem] (LMRS), l'Université de Rouen
 
Курс читается на английском языке. 
 
Организаторы: [[Кафедра теории динамических систем]] / [http://www.mi.ras.ru/ МИАН] / [http://www.mccme.ru/lifr/ Русско-французская лаборатория Poncelet] / [http://www.mccme.ru/ 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'')
# Ledrappier example (classical Riesz products). 
# Spectral type of the Morse substitution. 
# On the spectral type of subsitutions with (multi-dimensional Riesz products) with applications to interval exchange transformations.
# Host-Parreau-Méla theorem. 
# Spectral type of a rank one transformation via Bourgain technique.
# Bourgain singularity criterion. 
# Conditions for existence of the Lebesgue component.   
# 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.

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[http://mech.math.msu.su/department/tds/wiki/images/e/e0/CourseElHouceinR1.pdf Программа курса в PDF]

[http://www.mccme.ru/head/address.html Как добраться?]

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