# In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc

@article{Nikolski2012InAS,
title={In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc},
author={Nikolai K. Nikolski},
journal={Annales de l'Institut Fourier},
year={2012},
volume={62},
pages={1601-1626}
}
• N. Nikolski
• Published 2012
• Mathematics
• Annales de l'Institut Fourier
— Completeness of a dilation system (φ(nx))n>1 on the standard Lebesgue space L2(0, 1) is considered for 2-periodic functions φ. We show that the problem is equivalent to an open question on cyclic vectors of the Hardy space H(D2 ) on the Hilbert multidisc D2 . Several simple sufficient conditions are exhibited, which include however practically all previously known results (Wintner; Kozlov; Neuwirth, Ginsberg, and Newman; Hedenmalm, Lindquist, and Seip). For instance, each of the following…
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A Hardy space approach to the Nyman-Beurling and Báez-Duarte criterion for the Riemann Hypothesis (RH) was introduced in [16]. It states that the RH holds true if and only if the linear manifold N
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A correction to “In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc”
— This note corrects some inaccuracies remarked in the paper mentioned in the title. It contains also a few references to recent developments on the dilations f(nx) completeness problem and points
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