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UID:2520@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20181019T093000
DTEND;TZID=Europe/Paris:20181019T103000
DTSTAMP:20181004T073000Z
URL:https://www.i2m.univ-amu.fr/evenements/convergence-of-spherical-averag
 es-for-actions-of-fuchsian-groups/
SUMMARY: (...): Convergence of spherical averages for actions of Fuchsian g
 roups
DESCRIPTION::  Consider a measure-preserving action of a Fuchsian group G o
 n 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 tessell
 ation of the hyperbolic plane by images of R the boundaries between domain
 s comprise of complete geodesic lines. Our result now says that if the eve
 n corners condition holds\, then for any L^p-function f\, p>1\, its spheri
 cal averages of even orders converge almost surely.The main ingredient of 
 the proof is the construction of the new Markov coding for a Fuchsian grou
 p with the even corners condition. The key property of our coding is the f
 ollowing symmetry condition: the sequence of states generating an element 
 g^{-1} is obtained from the sequence for g as follows: we reverse the orde
 r 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
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