Book chapter
Transfer Operators with a Riesz Property
Transfer Operators, Endomorphisms, and Measurable Partitions, pp.105-111
Lecture Notes in Mathematics, Springer International Publishing
06/22/2018
DOI: 10.1007/978-3-319-92417-5_9
Abstract
A well known theorem (Riesz) in analysis states that every positive linear functional L on continuous functions is represented by a Borel measure. More precisely, let X be a locally compact Hausdorff space and Cc(X) the space of continuous functions with compact support. Then the well-known Riesz representation theorem from analysis says that, for every positive linear functional L, there exists a unique regular Borel measure μ on X such that L(f)=∫Xfdμ.\documentclass[12pt]{minimal}
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$$\displaystyle L(f) = \int _X f\; d\mu. $$
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We are interested in a special case of functionals Lx defined on a function space by the formula Lx(f) = f(x). For Borel functions ℱ(X,ℬ)\documentclass[12pt]{minimal}
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$$\mathcal F(X, {\mathcal B})$$
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$$(X, {\mathcal B})$$
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Details
- Title: Subtitle
- Transfer Operators with a Riesz Property
- 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.105-111
- Series
- Lecture Notes in Mathematics
- DOI
- 10.1007/978-3-319-92417-5_9
- eISSN
- 1617-9692
- ISSN
- 0075-8434
- Publisher
- Springer International Publishing; Cham
- Language
- English
- Date published
- 06/22/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241043802771
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