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[null,"1.","Record Nr.",null,"UNINA9910300125203321"]
[null,null,"Autore",null,"Bezuglyi Sergey"]
[null,null,"Titolo",null,"Transfer Operators, Endomorphisms, and Measurable Partitions / / by Sergey Bezuglyi, Palle E. T. Jorgensen"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018"]
[null,null,"ISBN",null,"3-319-92417-6"]
[null,null,"Edizione",null,"[1st ed. 2018.]"]
[null,null,"Descrizione fisica",null,"1 online resource (X, 162 p. 7 illus.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 2217"]
[null,null,"Disciplina",null,"519.5"]
[null,null,"Soggetti",null,"Measure theory"]
[{"$nulls":4},"Functional analysis"]
[{"$nulls":4},"Mathematical statistics"]
[{"$nulls":4},"Probabilities"]
[{"$nulls":4},"Thermodynamics"]
[{"$nulls":4},"Operator theory"]
[{"$nulls":4},"Measure and Integration"]
[{"$nulls":4},"Functional Analysis"]
[{"$nulls":4},"Probability and Statistics in Computer Science"]
[{"$nulls":4},"Probability Theory and Stochastic Processes"]
[{"$nulls":4},"Operator Theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"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 "]
[{"$nulls":4},"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."]