Hilbert spaces of martingales supporting certain substitution-dynamical systems

Dorin Ervin Dutkay; Palle E.T Jorgensen

doi:10.1090/S1088-4173-05-00135-9

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Hilbert spaces of martingales supporting certain substitution-dynamical systems

Journal article

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Hilbert spaces of martingales supporting certain substitution-dynamical systems

Dorin Ervin Dutkay and Palle E.T Jorgensen

Conformal Geometry and Dynamics, Vol.9(2), pp.24-45

2005

DOI: 10.1090/S1088-4173-05-00135-9

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Abstract

Let X be a compact Hausdorff space. We study finite-to-one mappings r : X → X, onto X, and measures on the corresponding projective limit space X∞(r). We show that certain quasi-invariant measures on X∞(r) correspond in a one-to-one fashion to measures on X which satisfy two identities. Moreover, we identify those special measures on X∞(r) which are associated via our correspondence with a function V on X, a Ruelle transfer operator RV , and an equilibrium measure μV on X.

Details

Title: Subtitle: Hilbert spaces of martingales supporting certain substitution-dynamical systems
Creators: Dorin Ervin Dutkay
Palle E.T Jorgensen
Resource Type: Journal article
Publication Details: Conformal Geometry and Dynamics, Vol.9(2), pp.24-45
DOI: 10.1090/S1088-4173-05-00135-9
ISSN: 1088-4173
eISSN: 1088-4173
Language: English
Date published: 2005
Academic Unit: Mathematics
Record Identifier: 9983985810402771

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