Book chapter
Transfer Operators on L1 and L2
Transfer Operators, Endomorphisms, and Measurable Partitions, pp.59-76
Lecture Notes in Mathematics, Springer International Publishing
06/22/2018
DOI: 10.1007/978-3-319-92417-5_5
Abstract
Given a transfer operator (R, σ), it is of interest to find the measuresμ such that both R and σ induce operators in the corresponding Lp spaces, i.e., in Lp(X,ℬ,μ)\documentclass[12pt]{minimal}
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$$L^p(X, {\mathcal B}, \mu )$$
\end{document}. We turn to this below, but our main concern are the cases p = 1, p = 2, and p = ∞. When R is realized as an operator in L2(X,ℬ,μ)\documentclass[12pt]{minimal}
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$$L^2(X, {\mathcal B}, \mu )$$
\end{document}, for a suitable choice of μ, then it is natural to ask for the adjoint operator R∗ where “adjoint” is defined with respect to the L2(μ)-inner product.
Details
- Title: Subtitle
- Transfer Operators on L1 and L2
- 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.59-76
- Series
- Lecture Notes in Mathematics
- DOI
- 10.1007/978-3-319-92417-5_5
- eISSN
- 1617-9692
- ISSN
- 0075-8434
- Publisher
- Springer International Publishing; Cham
- Language
- English
- Date published
- 06/22/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241152502771
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