Transfer Operators, Endomorphisms, and Measurable Partitions

• Verfasst von: Bezuglyi, Sergey [VerfasserIn]
• Verfasst von: 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
• Gesamttitel/Reihe: Springer eBook Collection
• Gesamttitel/Reihe: SpringerLink : Bücher
• ISBN: 978-3-319-92417-5
• DOI: doi: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
• Bibliogr. Hinweis: 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
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

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

Abstract

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