Transfer Operators, Endomorphisms, and Measurable Partitions
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※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 1st ed. 2018 Series: Lecture Notes in Mathematics Author: Bezuglyi, Sergey / Jorgensen, Palle E. T. Publisher: Springer ISBN: 9783319924168 Cover: PAPERBACK Date: 2018年06月 DESCRIPTION 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. TABLE OF CONTENTS 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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