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Autore: |
Bezuglyi Sergey
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Titolo: |
Transfer Operators, Endomorphisms, and Measurable Partitions [[electronic resource] /] / by Sergey Bezuglyi, Palle E. T. Jorgensen
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Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
Edizione: | 1st ed. 2018. |
Descrizione fisica: | 1 online resource (X, 162 p. 7 illus.) |
Disciplina: | 519.5 |
Soggetto topico: | Measure theory |
Functional analysis | |
Mathematical statistics | |
Probabilities | |
Thermodynamics | |
Operator theory | |
Measure and Integration | |
Functional Analysis | |
Probability and Statistics in Computer Science | |
Probability Theory and Stochastic Processes | |
Operator Theory | |
Persona (resp. second.): | JorgensenPalle E. T |
Nota di bibliografia: | Includes bibliographical references and index. |
Nota di contenuto: | 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. |
Sommario/riassunto: | 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. |
Titolo autorizzato: | Transfer operators, endomorphisms, and measurable partitions ![]() |
ISBN: | 3-319-92417-6 |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 996466758303316 |
Lo trovi qui: | Univ. di Salerno |
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