Transfer Operators, Endomorphisms, and Measurable Partitions

• Main Authors: Bezuglyi, Sergey (Author, http://id.loc.gov/vocabulary/relators/aut), Jorgensen, Palle E. T. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2217
• Subjects: Measure theory.; Functional analysis.; Mathematical statistics.; Probabilities.; Thermodynamics.; Operator theory.; Measure and Integration.; Functional Analysis.; Probability and Statistics in Computer Science.; Probability Theory and Stochastic Processes.; Operator Theory.

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...

Table of 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.