On the convergence of the rotated one-sided ergodic Hilbert transform
Résumé
Sufficient conditions have been given for the convergence in norm and a.e. of the ergodic Hilbert transform (\cite{G96}, \cite{CL}, \cite{Cu09}). Here we apply these conditions to the rotated ergodic Hilbert transform $\sum_{n=1}^\infty \frac{\lambda^n}{n} T^nf$, where $\lambda$ is a complex number of modulus 1. When $T$ is a contraction in a Hilbert space, we show that the logarithmic Hausdorff dimension of the set of $\lambda$'s for which this series does not converge is at most 2 and give examples where this bound is attained.
Domaines
Théorie spectrale [math.SP]
Origine : Fichiers produits par l'(les) auteur(s)
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