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A Note on Cyclic Vectors for the Shift

John R. Akeroyd,
Published in Taylor and Francis
Volume: 48

Issue: 3
Abstract

We strengthen a result in the literature that gives a necessary condition for the shift on the Hardy space H 2 ( G ) of some bounded, simply connected region G to be cyclic. Part of this involves a characterization, in terms of ‘ G , of what it means for G to be the image of under a conformal map whose boundary values are univalent a.e. m (normalized Lebesgue measure on ).