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Spectral disjointness of the powers of a class of rank one maps and Möbius disjointness.

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Publicado em Tue Dec 18 13:46:56 GMT-03:00 2012
Formatos:  FLV (640 X 360 px)

Spectral disjointness of the powers of a class of rank one maps and Möbius disjointness. El Houcein El Abdalaoui - Laboratoire de Mathématiques Raphaël Salem - Université de Rouen

In this talk, I will present my recent work with Mariusz Lemanczyk and Thierry de la Rue, in which it is proved that if T is weak mixing maps and T is in the class of rank one maps with bounded parameters then the powers of T are spectrally disjoint. As a consequence, we obtain a new proof of Bourgain Theorem(2011) on the orthogonality of this class to the Möbius function in the sens of Sarnak.Therefore, our work is connected to the Sarnak conjecture on the Möbius disjointness. A more details on this conjecture will be given.