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X-WR-CALNAME;VALUE=TEXT: -- Institut de MathÃ©matiques de Marseille\, UMR 7373
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SUMMARY:Alexey KLIMENKO - Convergence of spherical averages for actions of Fuchsian groups
UID:20181017T085218-a746-e2541@https://www.i2m.univ-amu.fr
DTSTAMP:20181017T085218
DTSTART:20181019T093000
DTEND:20181019T103000
CREATED:20181017T085218
ATTENDEE;CN=Alexey KLIMENKO:mailto:no-reply@math.cnrs.fr
LAST-MODIFIED:20181017T085218
LOCATION:FRUMAM
DESCRIPTION:Consider a measure-preserving action of a Fuchsian group G on a Lebesgue probability space X. Given a fundamental domain R\, we obtain a symmetric generating set consisting of all group elements that map R to adjacent domains. This generating set endows the group G with the norm\, and for a function f on X\, we define its spherical average of order n as the average with equal weights of f shifted by all elements in G with the norm n. Assume now that R has even corners\, that is\, that for the tessellation of the hyperbolic plane by images of R the boundaries between domains comprise of complete geodesic lines. Our result now says that if the even corners condition holds\, then for any L^p-function f\, p>1\, its spherical averages of even orders converge almost surely. The main ingredient of the proof is the construction of the new Markov coding for a Fuchsian group with the even corners condition. The key property of our coding is the following symmetry condition : the sequence of states generating an element g^-1 is obtained from the sequence for g as follows : we reverse the order of its terms and apply an involution on the state space to each of these terms. - The talk is based on the joint work with A. Bufetov and C. Series (arXiv:1805.11743).- http://www.hse.ru/en/org/persons/36852818 Alexey KLIMENKO [
CATEGORIES:(Agenda ERC IChaos|textebrut|filtrer_ical)]
URL:https://www.i2m.univ-amu.fr/Agenda-ERC-IChaos?id_evenement=2541
SEQUENCE:0
STATUS:CONFIRMED
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