LEADER 03436cam a2200397Ki 4500
008 180430s2018 sz b 001 0 eng d
z| 9783319924175 q| (eBook)
a| (OCoLC)1032591105 z| (OCoLC)1032670675
a| YDX b| eng e| rda c| YDX d| BDX d| OHX d| QGJ d| UMS d| OCLCF d| VA@ d| NUI d| STF d| PAU
a| QA3 b| .L28 no.2217
a| Bezuglyi, Sergey, d| 1954- e| author.
a| Transfer operators, endomorphisms, and measurable partitions / c| Sergey Bezuglyi, Palle E.T. Jorgensen.
a| Cham, Switzerland : b| Springer, c| 
a| x, 160 pages ; c| 24 cm.
a| text b| txt 2| rdacontent
a| unmediated b| n 2| rdamedia
a| volume b| nc 2| rdacarrier
a| Lecture notes in mathematics, x| 0075-8434 ; v| 2217
a| Includes bibliographical references and index.
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.
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.
a| Transfer operators.
a| Endomorphisms (Group theory)
a| Endomorphisms (Group theory) 2| fast 0| (OCoLC)fst00909788
a| Transfer operators. 2| fast 0| (OCoLC)fst01154612
a| Jørgensen, Palle E. T., d| 1947- e| author.
a| Lecture notes in mathematics (Springer-Verlag) ; v| 2217. x| 0075-8434
a| C0 b| PAU