LEADER 04964nam 22007335 450 001 996466758303316 005 20200706015833.0 010 $a3-319-92417-6 024 7 $a10.1007/978-3-319-92417-5 035 $a(CKB)3810000000358725 035 $a(DE-He213)978-3-319-92417-5 035 $a(MiAaPQ)EBC6296954 035 $a(PPN)229494102 035 $a(EXLCZ)993810000000358725 100 $a20180621d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTransfer Operators, Endomorphisms, and Measurable Partitions$b[electronic resource] /$fby Sergey Bezuglyi, Palle E. T. Jorgensen 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (X, 162 p. 7 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2217 311 $a3-319-92416-8 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aThe subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the ?easier? and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2217 606 $aMeasure theory 606 $aFunctional analysis 606 $aMathematical statistics 606 $aProbabilities 606 $aThermodynamics 606 $aOperator theory 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aProbability and Statistics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17036 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aThermodynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21050 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 615 0$aMeasure theory. 615 0$aFunctional analysis. 615 0$aMathematical statistics. 615 0$aProbabilities. 615 0$aThermodynamics. 615 0$aOperator theory. 615 14$aMeasure and Integration. 615 24$aFunctional Analysis. 615 24$aProbability and Statistics in Computer Science. 615 24$aProbability Theory and Stochastic Processes. 615 24$aThermodynamics. 615 24$aOperator Theory. 676 $a519.5 700 $aBezuglyi$b Sergey$4aut$4http://id.loc.gov/vocabulary/relators/aut$0150946 702 $aJorgensen$b Palle E. T$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466758303316 996 $aTransfer operators, endomorphisms, and measurable partitions$91749877 997 $aUNISA