@inproceedings{68a24e9ddcdb4d96aa628472dd4d9d1e,

title = "The one-sided ergodic Hilbert transform of normal contractions",

abstract = "Let T be a normal contraction on a Hilbert space H. For f ∈ H we study the one-sided ergodic Hilbert transform (Formula Presented). We prove that weak and strong convergence are equivalent, and show that the convergence is equivalent to convergence of the series (Formula Presented). When (Formula Presented), the transform is shown to be precisely minus the infinitesimal generator of the strongly continuous semi-group {(I − T)r}r≥0. The equivalence of weak and strong convergence of the transform is proved also for T an isometry or the dual of an isometry. For a general contraction T, we obtain that convergence of the series (Formula Presented) implies strong convergence of (Formula Presented).",

keywords = "Normal contractions, One-sided ergodic Hilbert transform",

author = "Guy Cohen and Michael Lin",

note = "Publisher Copyright: {\textcopyright} 2009 Birkh{\"a}user Verlag Basel/Switzerland.; International Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007 ; Conference date: 09-07-2007 Through 13-07-2007",

year = "2010",

month = jan,

day = "1",

doi = "10.1007/978-3-0346-0183-2_4",

language = "English",

isbn = "9783034601825",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing",

pages = "77--98",

editor = "Daniel Alpay and Victor Vinnikov",

booktitle = "Characteristic Functions, Scattering Functions and Transfer Functions",

}