Bufetov, Alexander I., Klimenko, Alexey and Series, Caroline (2023) Convergence of spherical averages for actions of Fuchsian groups. Commentarii Mathematici Helvetici, 98 (1). pp. 41-134. doi:10.4171/cmh/548 ISSN 0010-2571.

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Abstract

We prove pointwise convergence of spherical averages for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen–Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving a reversible Markov chain to which methods previously introduced by the first author for the case of free groups may be applied.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
SWORD Depositor:	Library Publications Router
Journal or Publication Title:	Commentarii Mathematici Helvetici
Publisher:	European Mathematical Society - EMS - Publishing House GmbH
ISSN:	0010-2571
Official Date:	24 May 2023
Dates:	Date Event 24 May 2023 Published 24 May 2022 Accepted
Volume:	98
Number:	1
Page Range:	pp. 41-134
DOI:	10.4171/cmh/548
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	22 August 2023
Date of first compliant Open Access:	22 August 2023

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