Comptes Rendus
no. 6
Complex analysis/Functional analysis
Composition operators on Hilbert spaces of entire functions
[Opérateurs de composition sur les espaces de Hilbert de fonctions entières]

Présenté par : Jean-Pierre Demailly

Minh Luan Doan1 ; Le Hai Khoi1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 495-499.

In this Note, we introduce Hilbert spaces of entire functions in the complex plane C. We study composition operators on these spaces and obtain, in particular, criteria for the boundedness and compactness of such operators. Our results contain the corresponding results of Chacón et al. (2007) [1] as particular cases.

Dans cette Note, nous introduisons des espaces de Hilbert de fonctions entières dans le plan complexe C. Nous étudions les opérateurs de composition sur ces espaces et obtenons notamment des critères pour que ces opérateurs soient bornés ou compacts. Nous retrouvons les résultats correspondents de Chacón et al. (2007) [1] comme cas particuliers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.007

Minh Luan Doan 1 ; Le Hai Khoi 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore 
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Minh Luan Doan; Le Hai Khoi. Composition operators on Hilbert spaces of entire functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 495-499. doi : 10.1016/j.crma.2015.03.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.007/

[1] G.A. Chacón; G.R. Chacón; J. Giménez Composition operators on spaces of entire functions, Proc. Amer. Math. Soc., Volume 135 (2007) no. 7, pp. 2205-2218

[2] K.C. Chan; J.H. Shapiro The cyclic behaviour of translation operators on Hilbert spaces of entire functions, Indiana Univ. Math. J., Volume 40 (1991) no. 4, pp. 1421-1449

[3] C.C. Cowen; B.I. MacCluer Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, USA, 1995

[4] B.Ya. Levin Lectures on Entire Functions, Transl. Math. Mononogr., Amer. Math. Soc., Providence, RI, 1996

[5] G. Pólya On an integral function of an integral function, J. Lond. Math. Soc., Volume 1 (1926), pp. 12-15

  • Pin Lin Tan; Le Hai Khoi Bounded Composition Operators on General Weighted Hardy Spaces, Complex Analysis and Operator Theory, Volume 14 (2020) no. 5 | DOI:10.1007/s11785-020-01009-y
  • Manjul Gupta; Deepika Baweja Composition and translation operators on certain subspaces of the space of entire functions of bounded type, Collectanea Mathematica, Volume 70 (2019) no. 2, p. 323 | DOI:10.1007/s13348-018-0229-7
  • Minh Luan Doan; Le Hai Khoi Closed range and cyclicity of composition operators on Hilbert spaces of entire functions, Complex Variables and Elliptic Equations, Volume 63 (2018) no. 11, p. 1558 | DOI:10.1080/17476933.2017.1391799
  • Minh Luan Doan; Bingyang Hu; Le Hai Khoi; Hervé Queffélec Approximation numbers for composition operators on spaces of entire functions, Indagationes Mathematicae, Volume 28 (2017) no. 2, p. 294 | DOI:10.1016/j.indag.2016.07.003
  • Minh Luan Doan; Le Hai Khoi; Trieu Le Composition Operators on Hilbert Spaces of Entire Functions of Several Variables, Integral Equations and Operator Theory, Volume 88 (2017) no. 3, p. 301 | DOI:10.1007/s00020-017-2384-8
  • Minh Luan Doan; Le Hai Khoi Hilbert Spaces of Entire Functions and Composition Operators, Complex Analysis and Operator Theory, Volume 10 (2016) no. 1, p. 213 | DOI:10.1007/s11785-015-0497-0

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