03869nam a2200505 i 4500991003635169707536m o d cr cnu|||unuuu190404s2018 sz a ob 001 0 eng d9783319924175(electronic bk.)3319924176(electronic bk.)9783319924168(print)331992416810.1007/978-3-319-92417-5doib14363720-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.72423AMS 47-02Bezuglyi, Sergey150946Transfer operators, endomorphisms, and measurable partitions[e-book] /Sergey Bezuglyi, Palle E. T. JorgensenCham, Switzerland :Springer,20181 online resource (x, 162 pages) :illustrationstexttxtrdacontentcomputercrdamediaonline resourcecrrdacarriertext filePDFrdaLecture notes in mathematics,0075-8434 ;2217Includes bibliographical references and index1. 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. ExamplesThe 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 zeasiery 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 collaboratorsTransfer operatorsFunctional analysisMeasure theoryOperator theoryProbabilitiesThermodynamicsEndomorphisms (Group theory)Jørgensen, Palle E. T.Printed edition:9783319924168An electronic book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-3-319-92417-5.b1436372003-03-2204-04-19991003635169707536Transfer operators, endomorphisms, and measurable partitions1749877UNISALENTOle01304-04-19m@ -engsz 00