A correction to “In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc”
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 563-567.

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 out some old statements of V. Ya. Kozlov from early 1950’s still unproved.

Quelques inexactitudes dans l’article mentionné dans le titre sont corrigées, et une information sur les progrès récents dans le sujet (sur la complétude des dilatations f(nx)) est ajoutée. On discute également quelques assertions sur la complétude (de V. Ya. Kozlov, 1950) qu’on n’a pas réussi à démontrer jusqu’à nos jours.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3170
Classification: 32A35,  32A60,  42B30,  42C30,  47A16
Keywords: dilations completeness, Hilbert’s multidisc, Bohr transform, cyclic vectors, Riemann hypothesis
License: CC-BY-ND 4.0
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Nikolski, Nikolai. A correction to “In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc”. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 563-567. doi : 10.5802/aif.3170. https://aif.centre-mersenne.org/articles/10.5802/aif.3170/

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[2] Hanner, Olof On the uniform convexity of L p and l p , Ark. Mat., Tome 3 (1955) no. 19, pp. 239-244 | Zbl

[3] Kozlov, V. Ya. On the completeness of systems of functions {ϕ(nx)} in the space L 2 (0,2π), Doklady Akad. Nauk SSSR, Tome 61 (1948), pp. 977-980 | Zbl

[4] Kozlov, V. Ya. On the completeness of a system of functions of type {ϕ(nx)} in the space L 2 , Doklady Akad. Nauk SSSR, Tome 73 (1950), pp. 441-444 | Zbl

[5] Nikolski, Nikolai In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc, Ann. Inst. Fourier, Tome 62 (2012) no. 2, pp. 1601-1626 | DOI | Zbl

[6] Nikolski, Nikolai Binomials whose dilations generate H 2 (𝔻), Algebra and Analysis, Tome 29 (2017) no. 6, pp. 159-177

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