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Record Nr. |
UNISALENTO991003635169707536 |
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Autore |
Bezuglyi, Sergey |
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Titolo |
Transfer operators, endomorphisms, and measurable partitions [e-book] / Sergey Bezuglyi, Palle E. T. Jorgensen |
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ISBN |
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9783319924175 |
3319924176 |
9783319924168 |
3319924168 |
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Descrizione fisica |
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1 online resource (x, 162 pages) : illustrations |
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Collana |
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Lecture notes in mathematics, 0075-8434 ; 2217 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Transfer operators |
Functional analysis |
Measure theory |
Operator theory |
Probabilities |
Thermodynamics |
Endomorphisms (Group theory) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index |
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Nota di contenuto |
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1. Introduction and Examples ; 2. Endomorphisms and Measurable Partitions ; 3. Positive, and Transfer, Operators on Measurable Spaces: general properties ; 4.Transfer Operators on Measure Spaces ; 5. Transfer operators on L1 and L2 ; 6. Actions of Transfer Operators on the set of Borel Probability Measures ; 7. Wold's Theorem and Automorphic Factors of Endomorphisms ; 8. Operators on the Universal Hilbert Space Generated by Transfer Operators ; 9. Transfer Operators with a Riesz Property ; 10. Transfer Operators on the Space of Densities ; 11. Piecewise Monotone Maps and the Gauss Endomorphism ; 12. Iterated Function Systems and Transfer Operators ; 13. Examples |
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Sommario/riassunto |
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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 |
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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 zeasiery 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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