04939nam 22007335 450 991030012520332120200706015833.03-319-92417-610.1007/978-3-319-92417-5(CKB)3810000000358725(DE-He213)978-3-319-92417-5(MiAaPQ)EBC6296954(PPN)229494102(EXLCZ)99381000000035872520180621d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierTransfer Operators, Endomorphisms, and Measurable Partitions /by Sergey Bezuglyi, Palle E. T. Jorgensen1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (X, 162 p. 7 illus.) Lecture Notes in Mathematics,0075-8434 ;22173-319-92416-8 Includes bibliographical references and index.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 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.Lecture Notes in Mathematics,0075-8434 ;2217Measure theoryFunctional analysisMathematical statisticsProbabilitiesThermodynamicsOperator theoryMeasure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Probability and Statistics in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17036Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Thermodynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21050Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Measure 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.Thermodynamics.Operator Theory.519.5Bezuglyi Sergeyauthttp://id.loc.gov/vocabulary/relators/aut150946Jorgensen Palle E. Tauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300125203321Transfer operators, endomorphisms, and measurable partitions1749877UNINA