| Description |
1 online resource (368 pages) |
| Series |
De Gruyter Studies in Mathematics ; v. 6 |
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De Gruyter studies in mathematics.
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| Contents |
Chapter 1: Measure preserving and null preserving point mappings; 1.1 Von Neumann's mean ergodic theorem, ergodicity; 1.2 Birkhoff's ergodic theorem; 1.3 Recurrence; 1.4 Shift transformations and stationary processes; 1.5 Kingman's subadditive ergodic theorem and the multiplicative ergodic theorem of Oseledec; 1.6 Relatives of the maximal ergodic theorem; 1.7 Some general tools and principles; Chapter 2: Mean ergodic theory; 2.1 The mean ergodic theorem; 2.2 Uniform convergence; 2.3 Weak mixing, continuous spectrum and multiple recurrence |
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2.4 The splitting theorem of Jacobs-Deleeuw-GlicksbergChapter 3: Positive contractions in L1; 3.1 The Hopf decomposition; 3.2 The Chacon-Ornstein theorem; 3.3 Brunel's lemma and the identification of the limit; 3.4 Existence of finite invariant measures; 3.5 The subadditive ergodic theorem for positive contractions in L1; 3.6 An example with divergence of Cesàro averages; 3.7 More on the filling scheme; Chapter 4: Extensions of the L1-theory; 4.1 Non positive contractions in L1; 4.2 Vector valued ergodic theorems; 4.3 Power bounded operators and harmonic functions |
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Chapter 5: Operators in C(K) and in Lp, (1<p<∞) 5.1 Markov operators in C(K); 5.2 Contractions in Lp, (1 <p < ∞); Chapter 6: Pointwise ergodic theorems for multiparameter and amenable semigroups; 6.1 Unrestricted convergence for averages over d-dimensional intervals; 6.2 Multiparameter additive and subadditive processes; 6.3 Multiparameter semigroups of L1-contractions; 6.4 Amenable semigroups; Chapter 7: Local ergodic theorems and differentiation; 7.1 Positive 1-parameter semigroups |
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7.2 Local ergodic theorems for multiparameter and non positive semigroups, and for vector valued functionsChapter 8: Subsequences and generalized means; 8.1 Strong convergence and mixing; 8.2 Pointwise convergence; Chapter 9: Special topics; 9.1 Ergodic theorems in von Neumann algebras; 9.2 Entropy and information; 9.3 Nonlinear nonexpansive mappings; 9.4 Miscellanea; Supplement: Harris Processes, Special Functions, Zero-Two-Law (by Antoine Brunei); Bibliography; Notation; Index |
| Summary |
Ergodic Theorems (De Gruyter Studies in Mathematics) |
| Subject |
Ergodic theory.
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Ergodic theory
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| Form |
Electronic book
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| Author |
Brunel, Antoine
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| ISBN |
9783110844641 |
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3110844648 |
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