Von Neumann and Birkhoff ergodic theorems for negatively curved groups

Lewis Bowen; Amos Nevo

doi:https://doi.org/10.24033/asens.2267

Von Neumann and Birkhoff ergodic theorems for negatively curved groups

Lewis Bowen, Amos Nevo

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We prove maximal inequalities for concentric ball and spherical shell averages on a general Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an additional condition, satisfied for example by all groups acting isometrically and properly discontinu-ously on CAT(1) spaces, we prove a pointwise ergodic theorem with respect to a sequence of proba-bility measures supported on concentric spherical shells.

Original language	English
Pages (from-to)	1113-1147
Number of pages	35
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	48
Issue number	5
DOIs	https://doi.org/10.24033/asens.2267
State	Published - 1 Sep 2015

All Science Journal Classification (ASJC) codes

Mathematics(all)

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https://doi.org/10.24033/asens.2267

Cite this

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title = "Von Neumann and Birkhoff ergodic theorems for negatively curved groups",

abstract = "We prove maximal inequalities for concentric ball and spherical shell averages on a general Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an additional condition, satisfied for example by all groups acting isometrically and properly discontinu-ously on CAT(1) spaces, we prove a pointwise ergodic theorem with respect to a sequence of proba-bility measures supported on concentric spherical shells.",

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AU - Bowen, Lewis

AU - Nevo, Amos

PY - 2015/9/1

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AB - We prove maximal inequalities for concentric ball and spherical shell averages on a general Gromov hyperbolic group, in arbitrary probability preserving actions of the group. Under an additional condition, satisfied for example by all groups acting isometrically and properly discontinu-ously on CAT(1) spaces, we prove a pointwise ergodic theorem with respect to a sequence of proba-bility measures supported on concentric spherical shells.

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SN - 0012-9593

VL - 48

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JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 5

ER -

Von Neumann and Birkhoff ergodic theorems for negatively curved groups

Abstract

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