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＜電子ブック＞
Transfer Operators, Endomorphisms, and Measurable Partitions / by Sergey Bezuglyi, Palle E. T. Jorgensen
(Lecture Notes in Mathematics. ISSN:16179692 ; 2217)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
本文言語	英語
大きさ	X, 162 p. 7 illus : online resource
著者標目	*Bezuglyi, Sergey author Jorgensen, Palle E. T author SpringerLink (Online service)
件　名	LCSH:Measure theory LCSH:Functional analysis LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Mathematical statistics LCSH:Probabilities LCSH:Thermodynamics LCSH:Operator theory FREE:Measure and Integration FREE:Functional Analysis FREE:Probability and Statistics in Computer Science FREE:Probability Theory FREE:Thermodynamics FREE:Operator Theory
一般注記	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 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 classesof 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 HTTP:URL=https://doi.org/10.1007/978-3-319-92417-5

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