Book chapter
Actions of Transfer Operators on the Set of Borel Probability Measures
Transfer Operators, Endomorphisms, and Measurable Partitions, pp.77-83
Lecture Notes in Mathematics, Springer International Publishing
06/22/2018
DOI: 10.1007/978-3-319-92417-5_6
Abstract
Let (R, σ) be a transfer operator defined on the space of Borel functions ℱ(X,ℬ)\documentclass[12pt]{minimal}
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$$\mathcal F(X, {\mathcal B})$$
\end{document}. The main theme of this chapter is the study of a dual action of R on the set of probability measures M1=M1(X,ℬ)\documentclass[12pt]{minimal}
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$$M_1 = M_1(X, {\mathcal B})$$
\end{document}. As a matter of fact, a big part of our results in this chapter remains true for any sigma-finite measure on (X,ℬ)\documentclass[12pt]{minimal}
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$$(X, {\mathcal B})$$
\end{document}, but we prefer to work with probability measures. The justification of this approach is contained in the results of Chap. 10.1007/978-3-319-92417-5_5 where we showed that the replacement of a measure by a probability measure does not affect the properties of R described in terms of measures. Our main assumption for this chapter is that the transfer operators R are normalized, that is R(1) = 1. In other chapters, we also used this assumption to prove some results.
Details
- Title: Subtitle
- Actions of Transfer Operators on the Set of Borel Probability Measures
- Creators
- Sergey Bezuglyi - University of IowaPalle E. T Jorgensen - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Transfer Operators, Endomorphisms, and Measurable Partitions, pp.77-83
- Series
- Lecture Notes in Mathematics
- DOI
- 10.1007/978-3-319-92417-5_6
- eISSN
- 1617-9692
- ISSN
- 0075-8434
- Publisher
- Springer International Publishing; Cham
- Language
- English
- Date published
- 06/22/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241157402771
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