Transfer Operators, Endomorphisms, and Measurable Partitions

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Transfer Operators, Endomorphisms, and Measurable Partitions by Sergey Bezuglyi, Palle E. T. Jorgensen, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Sergey Bezuglyi, Palle E. T. Jorgensen ISBN: 9783319924175
Publisher: Springer International Publishing Publication: June 21, 2018
Imprint: Springer Language: English
Author: Sergey Bezuglyi, Palle E. T. Jorgensen
ISBN: 9783319924175
Publisher: Springer International Publishing
Publication: June 21, 2018
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Embedded Engineering Education by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book The Maize Genome by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Max Weber's Vision for Bureaucracy by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Optical Switching in Next Generation Data Centers by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Re-Thinking Time at the Interface of Physics and Philosophy by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Liquid Crystal Colloids by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Baseline of Russian Arctic Laws by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book The Credibility of Sovereignty – The Political Fiction of a Concept by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Scalable Pattern Recognition Algorithms by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Treatment of Foreign Law - Dynamics towards Convergence? by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Knowledge-Intensive Entrepreneurship by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Advances in 3D Geoinformation by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Cartilage Regeneration by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Higher Education and Social Justice by Sergey Bezuglyi, Palle E. T. Jorgensen
Cover of the book Heat Transfer of Laminar Mixed Convection of Liquid by Sergey Bezuglyi, Palle E. T. Jorgensen
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy