Dissipative conformal measures on locally compact spaces

TY - JOUR

T1 - Dissipative conformal measures on locally compact spaces

AU - Thomsen, Klaus

PY - 2016

Y1 - 2016

N2 - The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which there are gauge invariant -KMS weights on a simple graph -algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

AB - The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which there are gauge invariant -KMS weights on a simple graph -algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

UR - http://www.scopus.com/inward/record.url?scp=84909953038&partnerID=8YFLogxK

U2 - 10.1017/etds.2014.73

DO - 10.1017/etds.2014.73

M3 - Journal article

SN - 0143-3857

VL - 36

SP - 649

EP - 670

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 2

ER -