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03385aam a2200349Mi 4500 001 F6F68974E96D11E8978F920F97128E48 003 SILO 005 20181116010210 008 180430s2018 sz a b 001 0 eng d 010 $a 2018944127 020 $a 9783319924168 020 $a 3319924168 035 $a (OCoLC)1032591105 040 $a YDX $b eng $e rda $c YDX $d BDX $d OHX $d QGJ $d UMS $d OCLCF $d VA@ $d NUI $d SILO 050 4 $a QA3 $b .L28 no.2217 100 1 $a Bezuglyi, Sergey, $d 1954- $e author. 245 10 $a Transfer operators, endomorphisms, and measurable partitions / $c Sergey Bezuglyi, Palle E. T. Jorgensen. 264 1 $a Cham, Switzerland : $b Springer, $c 2018. 300 $a x, 160 pages : $b illustrations ; $c 24 cm. 490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2217 504 $a Includes bibliographical references and index. 505 0 $a 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. 520 $a 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. 650 0 $a Transfer operators. 650 0 $a Endomorphisms (Group theory) 650 7 $a Endomorphisms (Group theory) $2 fast $0 (OCoLC)fst00909788 650 7 $a Transfer operators. $2 fast $0 (OCoLC)fst01154612 700 1 $a Jørgensen, Palle E. T., $d 1947- $e author. 830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2217. $x 0075-8434 941 $a 1 952 $l OVUX522 $d 20190212020939.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=F6F68974E96D11E8978F920F97128E48Initiate Another SILO Locator Search