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Spectral characterization of Wiener–Wintner dynamical systems

Published online by Cambridge University Press:  09 March 2004

I. ASSANI
I. ASSANI
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA (e-mail: assani@math.unc.edu)
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Abstract

Let $(X,\mathcal{B},\mu, T)$ be an ergodic dynamical system on the finite measure space $(X,\mathcal{B},\mu,T)$ and $\mathcal{K}$ its Kronecker factor. We denote by U the restriction of T onto $\mathcal{K}^{\perp}$ the orthocomplement of $\mathcal{K}$. 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 almost everywhere continuity of the fractional rotated ergodic Hilbert transform. The study of the L2 case leads to new classes of dynamical systems.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004 , pp. 347 - 365
Copyright
2004 Cambridge University Press

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