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 "e;easier"e; 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.
Transfer Operators, Endomorphisms, and Measurable Partitions
Laddas ned direkt
Läs i vår app för iPhone, iPad och Android
- ISBN: 9783319924175
- Förlag: Springer International Publishing
- Tillgängliga elektroniska format: Epub - Adobe DRM
Fler böcker inom Funktionell analys & transformationer (inom Kalkyl & matematisk analys), Integralkalkyl & integralekvationer (inom Kalkyl & matematisk analys), Sannolikhetskalkyl & matematisk statistik (inom Matematik), Stokastik (inom Tillämpad matematik), Termodynamik & värme (inom Fysik), Matematik- & statistikprogram (inom Affärstillämpningar), Matematik för datavetare (inom Matematisk databehandlingsteori)