Transfer Operators, Endomorphisms, and Measurable Partitions
Format: Paperback
ISBN13: 9783319924168
Paperback|9783319924168
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Overview
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 classesof 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.
The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classesof 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.
| ISBN-13 | 9783319924168 |
|---|---|
| ISBN-10 | 3319924168 |
| Weight | 0.56 Pounds |
| Dimensions | 6.10 x 0.39 x 9.25 In |
| List Price | $44.99 |
| Edition | 1st Edition |
| Format | Paperback |
|---|---|
| Language | English |
| Pages | x, 162 pages |
| Publisher | Springer |
| Published On | 2018-06-22 |
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