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

Doan, Minh Luan1 ; Khoi, Le Hai1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore
Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 495-499.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.007
Doan, Minh Luan 1 ; Khoi, Le Hai 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore 
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Doan, Minh Luan; Khoi, Le Hai. Composition operators on Hilbert spaces of entire functions. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 495-499. doi : 10.1016/j.crma.2015.03.007. http://archive.numdam.org/articles/10.1016/j.crma.2015.03.007/

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

[2] Chan, K.C.; Shapiro, J.H. 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] Cowen, C.C.; MacCluer, B.I. Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, USA, 1995

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

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

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