Bezuglyi, Sergey
Transfer operators, endomorphisms, and measurable partitions [Documento electrónico] / Sergey Bezuglyi, Palle E. T. Jorgensen. - Cham : Springer International Publishing : Springer , 2018 . - X, 162 p. : il.. - (Lecture Notes in Mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-319-92417-5
Matemática
Análise funcional
Informática
Distribuição (Teoria das probabilidades)
Termodinâmica
Teoria dos operadores
LCC QA312
Transfer operators, endomorphisms, and measurable partitions [Documento electrónico] / Sergey Bezuglyi, Palle E. T. Jorgensen. - Cham : Springer International Publishing : Springer , 2018 . - X, 162 p. : il.. - (Lecture Notes in Mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-319-92417-5
Matemática
Análise funcional
Informática
Distribuição (Teoria das probabilidades)
Termodinâmica
Teoria dos operadores
LCC QA312
