LEADER 03869nam a2200505 i 4500 001 991003635169707536 006 m o d 007 cr cnu|||unuuu 008 190404s2018 sz a ob 001 0 eng d 020 $a9783319924175$q(electronic bk.) 020 $a3319924176$q(electronic bk.) 020 $z9783319924168$q(print) 020 $z3319924168 024 7 $a10.1007/978-3-319-92417-5$2doi 035 $ab14363720-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.724$223 084 $aAMS 47-02 100 1 $aBezuglyi, Sergey$0150946 245 10$aTransfer operators, endomorphisms, and measurable partitions$h[e-book] /$cSergey Bezuglyi, Palle E. T. Jorgensen 264 1$aCham, Switzerland :$bSpringer,$c2018 300 $a1 online resource (x, 162 pages) :$billustrations 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 347 $atext file$bPDF$2rda 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2217 504 $aIncludes bibliographical references and index 505 0 $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 520 $aThe subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the zeasiery and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators 650 0$aTransfer operators 650 0$aFunctional analysis 650 0$aMeasure theory 650 0$aOperator theory 650 0$aProbabilities 650 0$aThermodynamics 650 0$aEndomorphisms (Group theory) 700 1 $aJørgensen, Palle E. T. 776 08$iPrinted edition:$z9783319924168 856 40$zAn electronic book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-3-319-92417-5 907 $a.b14363720$b03-03-22$c04-04-19 912 $a991003635169707536 996 $aTransfer operators, endomorphisms, and measurable partitions$91749877 997 $aUNISALENTO 998 $ale013$b04-04-19$cm$d@ $e-$feng$gsz $h0$i0