[Opérateurs de composition sur les espaces de Hilbert de séries entières de Dirichlet]
Dans cette Note, nous introduisons des espaces de Hilbert de séries entières de Dirichlet (à fréquences réelles) et considérons des opérateurs de composition sur ces espaces. Nous donnons des conditions nécessaires et suffisantes sur de telles séries pour avoir un ordre de Ritt égal à zéro, ainsi quʼun ordre logarithmique fini. Nous obtenons des critères dʼaction, de continuité, de compacité pour de tels opérateurs ou leurs différences.
In this Note, we introduce Hilbert spaces of entire Dirichlet series (with real frequencies) and consider composition operators on these spaces. We establish necessary and sufficient conditions for such series to have Ritt order zero, as well as a finite logarithmic order. Criteria for action, boundedness, compactness and compact difference of such operators are obtained.
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@article{CRMATH_2012__350_19-20_875_0,
author = {Hou, Xiaolu and Hu, Bingyang and Khoi, Le Hai},
title = {Composition operators on {Hilbert} spaces of entire {Dirichlet} series},
journal = {Comptes Rendus. Math\'ematique},
pages = {875--878},
publisher = {Elsevier},
volume = {350},
number = {19-20},
year = {2012},
doi = {10.1016/j.crma.2012.10.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.10.012/}
}
TY - JOUR AU - Hou, Xiaolu AU - Hu, Bingyang AU - Khoi, Le Hai TI - Composition operators on Hilbert spaces of entire Dirichlet series JO - Comptes Rendus. Mathématique PY - 2012 SP - 875 EP - 878 VL - 350 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.10.012/ DO - 10.1016/j.crma.2012.10.012 LA - en ID - CRMATH_2012__350_19-20_875_0 ER -
%0 Journal Article %A Hou, Xiaolu %A Hu, Bingyang %A Khoi, Le Hai %T Composition operators on Hilbert spaces of entire Dirichlet series %J Comptes Rendus. Mathématique %D 2012 %P 875-878 %V 350 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.10.012/ %R 10.1016/j.crma.2012.10.012 %G en %F CRMATH_2012__350_19-20_875_0
Hou, Xiaolu; Hu, Bingyang; Khoi, Le Hai. Composition operators on Hilbert spaces of entire Dirichlet series. Comptes Rendus. Mathématique, Tome 350 (2012) no. 19-20, pp. 875-878. doi : 10.1016/j.crma.2012.10.012. http://www.numdam.org/articles/10.1016/j.crma.2012.10.012/
[1] Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995
[2] Some properties of composition operators on entire Dirichlet series with real frequencies, C. R. Acad. Sci. Paris, Ser. I, Volume 350 (2012) no. 3–4, pp. 149-152
[3] Hilbert spaces of holomorphic Dirichlet series and applications to convolution equations, J. Math. Anal. Appl., Volume 206 (1997) no. 1, pp. 10-24
[4] On an integral function of an integral function, J. Lond. Math. Soc., Volume 1 (1926) no. 1, p. 12
[5] On entire Dirichlet series of zero order, Tôhoku Math. J. (2), Volume 18 (1966), pp. 144-155
[6] On certain points in the theory of Dirichlet series, Amer. J. Math., Volume 50 (1928) no. 1, pp. 73-86
[7] Compositions Operators and Classical Function Theory, Springer-Verlag, New York, 1993
[8] Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, vol. 13, Amer. Math. Soc., Providence, RI, 1974, pp. 49-128
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