Complementability of exponential systems

Yurii Belov

doi:10.1016/j.crma.2014.12.004

Complex analysis

Complementability of exponential systems

Presented by: 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 (Original language)
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.

Received: 2014-10-29
Accepted: 2014-12-19
Published online: 2015-01-07

DOI: 10.1016/j.crma.2014.12.004

Author's affiliations:

Yurii Belov 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 = {Yurii Belov},
     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},
}

TY  - JOUR
AU  - Yurii Belov
TI  - Complementability of exponential systems
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 215
EP  - 218
VL  - 353
IS  - 3
PB  - Elsevier
DO  - 10.1016/j.crma.2014.12.004
LA  - en
ID  - CRMATH_2015__353_3_215_0
ER  -

%0 Journal Article
%A Yurii Belov
%T Complementability of exponential systems
%J Comptes Rendus. Mathématique
%D 2015
%P 215-218
%V 353
%N 3
%I Elsevier
%R 10.1016/j.crma.2014.12.004
%G en
%F CRMATH_2015__353_3_215_0

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/

References
Cited by

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

[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 $L^{2} [- π, π]$ , J. Funct. Anal., Volume 130 (1995), pp. 131-160

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

Cited by Sources:

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

Comments - Policy