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

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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/}
}
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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/