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Transfer Operators, Endomorphisms, and Measurable Partitions / by Sergey Bezuglyi, Palle E. T. Jorgensen.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2366,2368-2379,2381-2382 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Bezuglyi, Sergey, 1954- author.
- Jørgensen, Palle E. T., 1947- author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2217.
- Lecture Notes in Mathematics, 0075-8434 ; 2217
- Language:
- English
- Subjects (All):
- Mathematics.
- Functional analysis.
- Computer science.
- Distribution (Probability theory).
- Thermodynamics.
- Operator theory.
- Measure and Integration.
- Functional Analysis.
- Probability and Statistics in Computer Science.
- Probability Theory and Stochastic Processes.
- Operator Theory.
- Local Subjects:
- Measure and Integration.
- Functional Analysis.
- Probability and Statistics in Computer Science.
- Probability Theory and Stochastic Processes.
- Thermodynamics.
- Operator Theory.
- Physical Description:
- 1 online resource (X, 162 pages) : 7 illustrations.
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2018.
- System Details:
- text file PDF
- 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 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 9783319924175
- Access Restriction:
- Restricted for use by site license.
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