Complementability of exponential systems

Yurii Belov

doi:10.1016/j.crma.2014.12.004

Complex analysis

Complementability of exponential systems
[Complémentabilité des systèmes d'exponentielles]

Présenté par : Gilles Pisier

Yurii Belov ¹

¹ Chebyshev Laboratory, St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia

Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 215-218.

Abstract (VO)
Résumé

We prove that any incomplete systems of complex exponentials ${e^{i λ_{n} t}}$ in $L^{2} (- π, π)$ is a subset of some complete and minimal system of exponentials. In addition, we prove an analogous statement for systems of reproducing kernels in de Branges spaces.

Nous démontrons que tout système incomplet d'exponentielles complexes ${e^{i λ_{n} t}}$ dans $L^{2} (- π, π)$ est un sous-ensemble d'un système complet et minimal d'exponentielles. De plus, nous montrons un résultat analogue pour des systèmes de noyaux reproduisants dans les espaces de de Branges.

Reçu le : 2014-10-29
Accepté le : 2014-12-19
Publié le : 2015-01-07

DOI : 10.1016/j.crma.2014.12.004

Affiliations des auteurs :

Yurii Belov ¹

¹ Chebyshev Laboratory, St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia

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     title = {Complementability of exponential systems},
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     number = {3},
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     doi = {10.1016/j.crma.2014.12.004},
     language = {en},
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Yurii Belov. Complementability of exponential systems. Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 215-218. doi : 10.1016/j.crma.2014.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.12.004/

Bibliographie
Cité par

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[10] K. Seip On the connection between exponential bases and certain related sequence in $L^{2} [- π, π]$ , J. Funct. Anal., Volume 130 (1995), pp. 131-160

[11] R. Young An Introduction to Nonharmonic Fourier Series, Academic Press, San Diego–London, 2001

Cité par Sources :

^☆ Author was supported by RNF grant 14-21-00035.

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