Transfer Operators, Endomorphisms, and Measurable Partitions

Autor: Sergey Bezuglyi, Palle Jorgensen

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Editura: Springer International Publishing AG

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The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an...

Informații despre carte

Autor

Sergey Bezuglyi, Palle Jorgensen

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2018

Pagini

162

EAN

9783319924168

ISBN

3319924168

Enbook ID

19382004

Editura

Springer International Publishing AG

Greutate

272

Dimensiuni

234 x 156 x 13

Descriere completă

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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Transfer Operators, Endomorphisms, and Measurable Partitions

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