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Ergodic theory and its connection with harmonic analysis : proceedings of the 1993 Alexandria conference /
Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1995.
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| Colección: | London Mathematical Society lecture note series ;
205. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; PART I SURVEY ARTICLES; Pointwise ergodic theorems via harmonic analysis; Introduction; Historical remarks; Prerequisites; How to use these notes; Acknowledgements; List of symbols; List of exercises; Chapter I. Good and bad sequences in periodic systems; 1. Ergodic sequences for periodic systems; Exercises for Example 1.4; 2. Sequences that are good in residue classes; Exercises for Example 1.12; 3. Sequences that are bad for periodic systems; Exercises for Example 1.18; Chapter II. Good sequences for mean L2 convergence; 1. Ergodic sequences
- Exercises for Example 2.22. Sequences that are good in the mean; Exercises for Example 2.11; Exercises for Example 2.15; 3. Notes on sequences bad in the mean; Exercises for Section 3; Notes to Chapter II; Chapter III. Universally good sequences for L1; Exercises for Example 3.2; Exercises for Example 3.7; Notes to Chapter III; Chapter IV. Universally good sequences for L2; 1. Ergodic, universally L2-good sequences; Exercises for Example 4.7; 2. The oscillation inequality; Exercises for Section 2; 3. The sequence of squares, I: The maximal inequality; Exercises for Section 3
- 4. The sequence of squares, II: The oscillation inequalityExercises for Section 4; Notes to Chapter IV; Chapter V. Universally bad sequences; 1. Banach principle and related matters; 2. Types of bad sequences; Notes to Chapter V; Chapter VI. The entropy method; 1. Bourgain's entropy method; 2. Application of entropy to constructing bad sequences; 3. Good and bad behavior of powers; Notes to Chapter VI; Chapter VII. Sequences that are good only for some Lp; References; Harmonic analysis in rigidity theory; 1. Introduction; 2. A Synopsis of Rigidity theory; 2.1. Early results.
- 2.2. Mostow's strong rigidity theorems.2.3. Margulis' super rigidity theorem.; 2.4. Further developments.; 2.4.1. Actions of semisimple groups and their lattice; 2.4.2. Riemannian geometry.; 2.4.3. Dynamics of amenable groups.; 3. Mautner's Phenomenon and Asymptotics of Matrix Coefficients; 3.1. The Mautner-Moore results.; 3.2. Asymptotics of matrix coefficients.; 3.3. Higher rank hyperbolic abelian actions.; 3.4. Restrictions of representations to lattices and equivariant maps.; 4. Amenability; 4.1. Definitions and basic results.; 4.2. Amenability, superrigidity and other applications.
- 5. Kazhdan's Property5.1. Definitions and basic results.; 5.2. Lorentz actions.; 5.3. Infinitesimal and local rigidity of actions.; 5.4. Discrete spectrum.; 5.5. Ruziewicz' problem.; 5.6. Gaps in the Hausdorff dimension of limit sets.; 5.7. Variants of Kazhdan's property.; 6. Miscellaneous Applications; 6.1. Isospectral rigidity.; 6.2. Entropy rigidity.; 6.3. Unitary representations with locally closed orbits.; References; Some properties and applications of joinings in ergodic theory; 0. Introduction; I. General study of joinings; II. Examples.; 1. Locally rank one transformations.