no. 2
A correction to “In a shadow of the RH: Cyclic vectors of Hardy spaces on the Hilbert multidisc”
Nikolski, Nikolai1
1 Université de Bordeaux UFR de Mathématiques et Informatique 351 cours de la Libération 33405 Talence (France)
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
Mot clés : complétude des dilatations, multidisque de Hilbert, transformation de Bohr, vecteurs cycliques, l’Hypothèse de Riemann

Nikolski, Nikolai 1

1 Université de Bordeaux UFR de Mathématiques et Informatique 351 cours de la Libération 33405 Talence (France)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/

[1] Bourgin, David Gordon A class of sequences of functions, Trans. Am. Math. Soc., Volume 60 (1946), pp. 478-518 | DOI | Zbl

[2] Hanner, Olof On the uniform convexity of L p and l p , Ark. Mat., Volume 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, Volume 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, Volume 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, Volume 62 (2012) no. 2, pp. 1601-1626 | DOI | Zbl

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

[7] Rudin, Walter Function theory in polydiscs, Mathematics Lecture Note Series, W. A. Benjamin, Inc, 1969, 188 pages | Zbl

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