[Opérateurs de composition sur les espaces de Hilbert de fonctions entières]
Dans cette Note, nous introduisons des espaces de Hilbert de fonctions entières dans le plan complexe . 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 . 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.
Accepté le :
Publié le :
@article{CRMATH_2015__353_6_495_0,
author = {Doan, Minh Luan and Khoi, Le Hai},
title = {Composition operators on {Hilbert} spaces of entire functions},
journal = {Comptes Rendus. Math\'ematique},
pages = {495--499},
publisher = {Elsevier},
volume = {353},
number = {6},
year = {2015},
doi = {10.1016/j.crma.2015.03.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.03.007/}
}
TY - JOUR AU - Doan, Minh Luan AU - Khoi, Le Hai TI - Composition operators on Hilbert spaces of entire functions JO - Comptes Rendus. Mathématique PY - 2015 SP - 495 EP - 499 VL - 353 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.03.007/ DO - 10.1016/j.crma.2015.03.007 LA - en ID - CRMATH_2015__353_6_495_0 ER -
%0 Journal Article %A Doan, Minh Luan %A Khoi, Le Hai %T Composition operators on Hilbert spaces of entire functions %J Comptes Rendus. Mathématique %D 2015 %P 495-499 %V 353 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.03.007/ %R 10.1016/j.crma.2015.03.007 %G en %F CRMATH_2015__353_6_495_0
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://www.numdam.org/articles/10.1016/j.crma.2015.03.007/
[1] Composition operators on spaces of entire functions, Proc. Amer. Math. Soc., Volume 135 (2007) no. 7, pp. 2205-2218
[2] 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] Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, USA, 1995
[4] Lectures on Entire Functions, Transl. Math. Mononogr., Amer. Math. Soc., Providence, RI, 1996
[5] On an integral function of an integral function, J. Lond. Math. Soc., Volume 1 (1926), pp. 12-15
Cité par Sources :
☆ Supported in part by MOE's AcRF Tier 1 grant M4011166.110 (RG24/13).
