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Transfer operators, endomorphisms, and measurable partitions

Author: Sergey Bezuglyi; Palle E T Jørgensen
Publisher: Cham, Switzerland : Springer, 2018.
Series: Lecture notes in mathematics (Springer-Verlag), 2217.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bezuglyi, Sergey, 1954-
Transfer operators, endomorphisms, and measurable partitions.
Cham, Switzerland : Springer, 2018
(OCoLC)1032591105
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sergey Bezuglyi; Palle E T Jørgensen
ISBN: 9783319924175 3319924176
OCLC Number: 1042073366
Description: 1 online resource (x, 162 pages) : illustrations
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2217.
Responsibility: Sergey Bezuglyi, Palle E.T. Jorgensen.

Abstract:

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.

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