Transfer Operators, Endomorphisms, and Measurable Partitions (1st ed. 2018) (Lecture Notes in Mathematics #2217)

Synopsis

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.

Copyright:

2018

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9783319924175

Related ISBNs:

9783319924168

Publisher:

Springer International Publishing

Date of Addition:

10/20/18

Copyrighted By:

Springer International Publishing AG

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Science, Computers and Internet, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.