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SPECTRAL CHARACTERIZATION OF WIENER WINTNER DYNAMICAL SYSTEMS
 

Summary: SPECTRAL CHARACTERIZATION OF WIENER WINTNER
DYNAMICAL SYSTEMS
BY I. ASSANI
Abstract. Let (X, B, , T) be an ergodic dynamical system on the finite measure space
(X, B, , T) and K its Kronecker factor. We denote by U the restriction of T onto K
the orthocomplement of K. We give a spectral characterization in L2
of Wiener Wintner
functions in terms of the capacity of the support of the maximal spectral type of U and
the a.e. continuity of the fractional rotated ergodic Hilbert transform. The study of the
L2
case leads to new classes of dynamical systems.
1. Introduction
In [A1] we introduced and studied ergodic dynamical systems that we called Wiener
Wintner dynamical systems of power type in Lp. We defined a function f to be a Wiener
Wintner function in the following way:
Definition 1: Let (X, B, , T) be an ergodic dynamical system. A function f is a Wiener-
Wintner function of power type in Lp if there exist finite positive constants Cf and
such that
sup

  

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

 

Collections: Mathematics