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Transfer Operators, Endomorphisms, and Measurable Partitions

  • Sergey Bezuglyi
  • Palle E. T. Jorgensen

Part of the Lecture Notes in Mathematics book series (LNM, volume 2217)

Table of contents

  1. Front Matter
    Pages i-x
  2. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 1-12
  3. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 13-21
  4. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 23-38
  5. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 39-58
  6. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 59-76
  7. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 77-83
  8. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 85-92
  9. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 93-104
  10. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 105-111
  11. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 113-117
  12. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 119-132
  13. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 133-142
  14. Sergey Bezuglyi, Palle E. T. Jorgensen
    Pages 143-149
  15. Back Matter
    Pages 151-162

About this book

Introduction

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.

Keywords

Endomorphisms of Measure Spaces Transfer Operators Invariant Measures Measurable Partitions Harmonic Functions

Authors and affiliations

  • Sergey Bezuglyi
    • 1
  • Palle E. T. Jorgensen
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of IowaIowa CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-92417-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-92416-8
  • Online ISBN 978-3-319-92417-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site