Comptes Rendus
no. 3
Complex analysis
Complementability of exponential systems
[Complémentabilité des systèmes d'exponentielles]

Présenté par : Gilles Pisier

Yurii Belov1
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.

Nous démontrons que tout système incomplet d'exponentielles complexes {eiλnt} dans L2(−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.

We prove that any incomplete systems of complex exponentials {eiλnt} in L2(−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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.12.004
Yurii Belov 1

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

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[2] A. Baranov; Y. Belov; A. Borichev Strong M-basis property for systems of reproducing kernels in de Branges spaces | arXiv

[3] Yu. Belov; T. Mengestie; K. Seip Unitary discrete Hilbert transforms, J. Anal. Math., Volume 112 (2010), pp. 383-395

[4] L. de Branges Hilbert Spaces of Entire Functions, Prentice–Hall, Englewood Cliffs, 1968

[5] S.V. Hruscev; N.K. Nikolskii; B.S. Pavlov Unconditional bases of exponentials and of reproducing kernels, Leningrad, 1979/1980 (Lecture Notes in Mathematics), Volume vol. 864, Springer, Berlin–New York (1981), pp. 214-335

[6] P. Koosis The Logarithmic Integral, I, Cambridge University Press, Cambridge, UK, 1988

[7] B.Ya. Levin Lectures on Entire Functions, Translations of Mathematical Monographs, vol. 150, American Mathematical Society, Providence, RI, USA, 1996

[8] A. Nakamura Basis properties and complements of complex exponential systems, Hokkaido Math. J., Volume 36 (2007) no. 1, pp. 193-206

[9] R. Redheffer Completeness of sets of complex exponentials, Adv. Math., Volume 24 (1977), pp. 1-62

[10] K. Seip On the connection between exponential bases and certain related sequence in L2[−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

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

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