Disintegration of projective measures

Authors:
Dorin Ervin Dutkay and Palle E. T. Jorgensen

Journal:
Proc. Amer. Math. Soc. **135** (2007), 169-179

MSC (2000):
Primary 42C40, 42A16, 42A65, 43A65, 46G15, 47D07, 60G18

Published electronically:
June 22, 2006

MathSciNet review:
2280185

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we study a class of quasi-invariant measures on paths generated by discrete dynamical systems. Our main result characterizes the subfamily of these measures which admit a certain disintegration. This is a disintegration with respect to a random walk Markov process which is indexed by the starting point of the paths. Our applications include wavelet constructions on Julia sets of rational maps on the Riemann sphere.

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Additional Information

**Dorin Ervin Dutkay**

Affiliation:
Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

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

Email:
jorgen@math.uiowa.edu

DOI:
https://doi.org/10.1090/S0002-9939-06-08469-3

Keywords:
Measures,
projective limits,
transfer operator,
martingale,
fixed-point

Received by editor(s):
August 16, 2004

Received by editor(s) in revised form:
July 29, 2005

Published electronically:
June 22, 2006

Additional Notes:
This work was supported in part by NSF grant DMS 0457491

Communicated by:
David R. Larson

Article copyright:
© Copyright 2006
American Mathematical Society