Geodesic
On composition operators on Hilbert spaces of entire functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 3-7.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a complete description of the families of continuous and compact composition operators on Hilbert spaces of entire functions introduced by K. Chan and J. Shapiro to study some dynamical properties of translation operators. In contrast to recent papers devoted to the same problems we do not use any additional assumptions on the spaces. We apply a new approach based on the embedding of a Hilbert space under consideration into some appropriate Banach space with sup-norm.
Keywords: entire functions, composition operators, weighted spaces. 
@article{IVM_2017_10_a0,
     author = {A. V. Abanin and T. I. Abanina},
     title = {On composition operators on {Hilbert} spaces of entire functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--7},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_10_a0/}
}
TY  - JOUR
AU  - A. V. Abanin
AU  - T. I. Abanina
TI  - On composition operators on Hilbert spaces of entire functions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 3
EP  - 7
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_10_a0/
LA  - ru
ID  - IVM_2017_10_a0
ER  - 
%0 Journal Article
%A A. V. Abanin
%A T. I. Abanina
%T On composition operators on Hilbert spaces of entire functions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 3-7
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_10_a0/
%G ru
%F IVM_2017_10_a0
A. V. Abanin; T. I. Abanina. On composition operators on Hilbert spaces of entire functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 3-7. http://geodesic.mathdoc.fr/item/IVM_2017_10_a0/

[1] Birkhoff G. D., “Démonstration d'un théoreme elementaire sur les fonctions entiéres”, C. R. Acad. Sci. Paris, 189 (1929), 473–475 | Zbl

[2] Chan K. C., Shapiro J., “The cyclic behavior of translation operators on Hilbert spaces of entire functions”, Indiana Univ. Math. J., 40:4 (1991), 1421–1449 | DOI | MR | Zbl

[3] Chacón G. A., Chacón G. R., Giménez J., “Composition operators on spaces of entire functions”, Proc. Amer. Math. Soc., 135:7 (2007), 2205–2218 | DOI | MR | Zbl

[4] Doan M. L., Khoi L. H., “Hilbert spaces of entire functions and compositions operators”, Complex Anal. Oper. Theory, 10:1 (2016), 213–230 | DOI | MR | Zbl

[5] Pólya G., “On an integral function of an integral function”, J. London Math. Soc., 1:1 (1926), 12–15 | DOI | MR | Zbl

[6] Fam Chong Tien, “Kompozitsionnye operatory v vesovykh banakhovykh prostranstvakh golomorfnykh funktsii”, Izv. vuzov. Sev.-Kavkazsk. region. Estestv. nauki, 2012, no. 6, 34–39