Wiener Wintner Ergodic Theorems

Download or read book Wiener Wintner Ergodic Theorems written by Idris Assani and published by World Scientific Publishing Company. This book was released on 2003-05-22 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiener Wintner ergodic theorem is a strengthening of Birkhoff pointwise ergodic theorem. Announced by N Wiener and A Wintner, this theorem has introduced the study of a general phenomenon in ergodic theory in which samplings are “good” for an uncountable number of systems. We study the rate of convergence in the uniform version of this theorem and what we call Wiener Wintner dynamical systems and prove for these systems two pointwise results: the a.e. double recurrence theorem and the a.e. continuity of the fractional rotated ergodic Hilbert transform. Some extensions of the Wiener Wintner ergodic theorem are also given.