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

Présenté par : Gilles Pisier

Belov, Yurii1
1 Chebyshev Laboratory, St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia
Comptes Rendus. Mathématique, Tome 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
Belov, Yurii 1

1 Chebyshev Laboratory, St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia 
@article{CRMATH_2015__353_3_215_0,
     author = {Belov, Yurii},
     title = {Complementability of exponential systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {215--218},
     publisher = {Elsevier},
     volume = {353},
     number = {3},
     year = {2015},
     doi = {10.1016/j.crma.2014.12.004},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2014.12.004/}
}
TY  - JOUR
AU  - Belov, Yurii
TI  - Complementability of exponential systems
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 215
EP  - 218
VL  - 353
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2014.12.004/
DO  - 10.1016/j.crma.2014.12.004
LA  - en
ID  - CRMATH_2015__353_3_215_0
ER  - 
%0 Journal Article
%A Belov, Yurii
%T Complementability of exponential systems
%J Comptes Rendus. Mathématique
%D 2015
%P 215-218
%V 353
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2014.12.004/
%R 10.1016/j.crma.2014.12.004
%G en
%F CRMATH_2015__353_3_215_0
Belov, Yurii. Complementability of exponential systems. Comptes Rendus. Mathématique, Tome 353 (2015) no. 3, pp. 215-218. doi : 10.1016/j.crma.2014.12.004. http://archive.numdam.org/articles/10.1016/j.crma.2014.12.004/

[1] Baranov, A.; Belov, Yu.; Borichev, A. Hereditary completeness for systems of exponentials and reproducing kernels, Adv. Math., Volume 235 (2013), pp. 525-554

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

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

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

[5] Hruscev, S.V.; Nikolskii, N.K.; Pavlov, B.S. 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] Koosis, P. The Logarithmic Integral, I, Cambridge University Press, Cambridge, UK, 1988

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

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

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

[10] Seip, K. On the connection between exponential bases and certain related sequence in L2[−π,π], J. Funct. Anal., Volume 130 (1995), pp. 131-160

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

Cité par Sources :

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