IRMA Lectures in Mathematics and Theoretical Physics 2009; 773 pp; hardcover Volume: 14 ISBN10: 3037190469 ISBN13: 9783037190463 List Price: US$128 Member Price: US$102.40 Order Code: EMSILMTP/14
 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 almosteverywhere 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 Part I. Spectral theorems and convergence in mean  The von Neumann theorem and spectral regularization
 Spectral representation of weakly stationary processes
Part II. Ergodic theorems  Dynamical systemsergodicity and mixing
 Pointwise ergodic theorems
 Banach principle and continuity principle
 Maximal operators and Gaussian processes
 The central limit theorem for dynamical systems
Part III. Methods arising from the theory of stochastic processes  The metric entropy method
 The majorizing measure method
 Gaussian processes
Part IV. Three studies  Riemann sums
 A study of the system \((f(nx))\)
 Divisors and random walks
 Bibliography
 Index
