This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost-everywhere convergence problems.

Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods, and results presented in this book of great interest. It is written in a style accessible to graduate students.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in dynamical systems.

Table of Contents

• The von Neumann theorem and spectral regularization
• Spectral representation of weakly stationary processes

• Dynamical systems--ergodicity and mixing
• Pointwise ergodic theorems
• Banach principle and continuity principle
• Maximal operators and Gaussian processes
• The central limit theorem for dynamical systems

• The metric entropy method
• The majorizing measure method
• Gaussian processes

• Riemann sums
• A study of the system $(f(nx))$
• Divisors and random walks
• Bibliography
• Index