## Hilbert spaces of martingales supporting certain substitution-dynamical systems

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- by Dorin Ervin Dutkay and Palle E. T. Jorgensen
- Conform. Geom. Dyn.
**9**(2005), 24-45 - DOI: https://doi.org/10.1090/S1088-4173-05-00135-9
- Published electronically: March 24, 2005
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## Abstract:

Let $X$ be a compact Hausdorff space. We study finite-to-one mappings $r\colon X\rightarrow X$, onto $X$, and measures on the corresponding projective limit space $X_\infty (r)$. We show that certain quasi-invariant measures on $X_\infty (r)$ correspond in a one-to-one fashion to measures on $X$ which satisfy two identities. Moreover, we identify those special measures on $X_\infty (r)$ which are associated via our correspondence with a function $V$ on $X$, a Ruelle transfer operator $R_V$, and an equilibrium measure $\mu _V$ on $X$.## References

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## Bibliographic Information

**Dorin Ervin Dutkay**- Affiliation: Department of Mathematics Hill Center-Busch Campus, Rutgers University, Piscataway, New Jersey 08845-8019
- MR Author ID: 608228
- Email: ddutkay@math.rutgers.edu
**Palle E. T. Jorgensen**- Affiliation: Department of Mathematics The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419
- MR Author ID: 95800
- ORCID: 0000-0003-2681-5753
- Email: jorgen@math.uiowa.edu
- Received by editor(s): January 23, 2005
- Received by editor(s) in revised form: February 2, 2005
- Published electronically: March 24, 2005
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**9**(2005), 24-45 - MSC (2000): Primary 42C40, 42A16, 42A65, 43A65, 46G15, 47D07, 60G18
- DOI: https://doi.org/10.1090/S1088-4173-05-00135-9
- MathSciNet review: 2133804

Dedicated: Dedicated to the memory of Shizuo Kakutani