Harmonic Analysis of Operators Associated with a Multiparameter Group of Dilations

Chapters in this book

1. Frontmatter I
2. A Zd Ergodic Theorem with Large Normalising Constants 1
3. A Repeated Filling Scheme for Upcrossings 15
4. When is a Transitive Map Chaotic? 25
5. Une Nouvelle Loi Forte des Grands Nombres 41
6. An Approximation Condition for Large Deviations and Some Applications 63
7. Sets of Recurrence and Generalized Polynomials 91
8. The Strong Arc-Sine Law in Higher Dimensions 111
9. Integer and Fractional Parts of Good Averaging Sequences in Ergodic Theory 117
10. The Uniqueness of Induced Operators 133
11. On Convergence of Partial Sums of Independent Random Variables 137
12. Harmonic Analysis of Operators Associated with a Multiparameter Group of Dilations 145
13. Markov Matrices 157
14. Existence and Continuity of the Quadratic Variation of Strong Martingales 179
15. Convergence Rate in the Strong Law of Large Numbers for Markov Chains 185
16. A Mean Ergodic Theorem for 1/NΣNn=1f(Tnx)g(Tn2x) 193
17. Convergence of Ergodic Averages 229
18. Bourgain's Entropy Criteria 249
19. Self-Intersections of Closed Geodesies on a Negatively Curved Surface: Statistical Regularities 263
20. A Note on the Law of the Iterated Logarithm for Weighted Sums of Independent Identically Distributed Random Variables 273
21. Besicovitch Functions and Weighted Ergodic Theorems for LCA Group Actions 277
22. A Remark on the Strong Sweeping Out Property 291
23. Ergodic Invertible Liftings 295
24. The Uniform Ergodic Theorem for Dynamical Systems 305
25. Pointwise Fourier Inversion and Related Jacobi Polynomial Expansions 333
26. The Distribution of the Particles of a Branching Random Walk 345
27. On a Random Ergodic Theorem for Bistochastic Operators 365
28. A Central Limit Theorem for Conditional Distributions 373
29. Complex Methods in the Calculation of Some Distribution Functions 381
30. Exponential Integrability of Rademacher Series 389
31. Weighted Averages of Contractions Along Subsequences 397
32. On Uniform Distribution of Sequences 405
33. Ergodic Theorems for Exit Laws 421
34. On Skew Products of Irrational Rotations with Tori 435