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.
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.
Accepted:
Published online:
Minh Luan Doan 1; Le Hai Khoi 1
@article{CRMATH_2015__353_6_495_0, author = {Minh Luan Doan and Le Hai Khoi}, 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}, }
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] 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
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☆ Supported in part by MOE's AcRF Tier 1 grant M4011166.110 (RG24/13).
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