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Transfer Operators, Endomorphisms, and Measurable Partitions / by Sergey Bezuglyi, Palle E. T. Jorgensen

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer eBook Collection | SpringerLink Bücher | Lecture notes in mathematics ; 2217Publisher: Cham : Springer, 2018Description: Online-Ressource (X, 162 p. 7 illus, online resource)ISBN:
  • 9783319924175
Subject(s): Additional physical formats: 9783319924168 | Erscheint auch als: 978-3-319-92416-8 Druck-Ausgabe | Erscheint auch als: Transfer operators, endomorphisms, and measurable partitions. Druck-Ausgabe Cham, Switzerland : Springer, 2018. x, 160 SeitenDDC classification:
  • 515.42
MSC: MSC: *37-02 | 28-02 | 37B10 | 37A05 | 37A30 | 37C30 | 47B65 | 28D05RVK: RVK: SI 850LOC classification:
  • QA312-312.5
DOI: DOI: 10.1007/978-3-319-92417-5Online resources: Summary: The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaboratorsSummary: Inhaltsverz.: 1. Introduction and Examples -- 2. Endomorphisms and Measurable Partitions -- 3. Positive, and Transfer, Operators on Measurable Spaces: general properties -- 4.Transfer Operators on Measure Spaces -- 5. Transfer operators on L1 and L2 -- 6. Actions of Transfer Operators on the set of Borel Probability Measures -- 7. Wold’s Theorem and Automorphic Factors of Endomorphisms -- 8. Operators on the Universal Hilbert Space Generated by Transfer Operators -- 9. Transfer Operators with a Riesz Property -- 10. Transfer Operators on the Space of Densities -- 11. Piecewise Monotone Maps and the Gauss Endomorphism -- 12. Iterated Function Systems and Transfer Operators -- 13. ExamplesPPN: PPN: 1026847850Package identifier: Produktsigel: ZDB-2-LNM | ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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