| Online-Ressource |
Verfasst von: | Bezuglyi, Sergey [VerfasserIn] |
| Jorgensen, Palle E. T. [VerfasserIn] |
Titel: | Transfer Operators, Endomorphisms, and Measurable Partitions |
Verf.angabe: | by Sergey Bezuglyi, Palle E. T. Jorgensen |
Verlagsort: | Cham |
Verlag: | Springer |
Jahr: | 2018 |
Umfang: | Online-Ressource (X, 162 p. 7 illus, online resource) |
Gesamttitel/Reihe: | Lecture Notes in Mathematics ; 2217 |
| Springer eBook Collection |
| SpringerLink : Bücher |
ISBN: | 978-3-319-92417-5 |
Abstract: | 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 collaborators |
| 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. Examples |
DOI: | doi:10.1007/978-3-319-92417-5 |
URL: | Volltext: http://dx.doi.org/10.1007/978-3-319-92417-5 |
| Resolving-System ; Verlag: https://doi.org/10.1007/978-3-319-92417-5 |
| Inhaltstext: https://zbmath.org/?q=an:1416.37002 |
| DOI: https://doi.org/10.1007/978-3-319-92417-5 |
Schlagwörter: | (s)Transferoperator / (s)Endomorphismus / (s)Maßtheorie |
Datenträger: | Online-Ressource |
Sprache: | eng |
Bibliogr. Hinweis: | Erscheint auch als : Druck-Ausgabe |
| Erscheint auch als : Druck-Ausgabe: Bezuglyj, Sergej I., 1954 - : Transfer operators, endomorphisms, and measurable partitions. - Cham, Switzerland : Springer, 2018. - x, 160 Seiten |
K10plus-PPN: | 1026847850 |
Verknüpfungen: | → Übergeordnete Aufnahme |
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Lokale URL UB: | Zum Volltext |
Transfer Operators, Endomorphisms, and Measurable Partitions / Bezuglyi, Sergey [VerfasserIn]; 2018 (Online-Ressource)