Comptes Rendus
Complex analysis/Functional analysis
Composition operators on Hilbert spaces of entire functions
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.

Received:
Accepted:
Published online:
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

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Supported in part by MOE's AcRF Tier 1 grant M4011166.110 (RG24/13).

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