The paper gives a complete characterization of all unitary operators acting in some wide Hilbert spaces $A^2_\omega(\mathbb{C})$ of entire functions possessing weighted square integrable modulus over the whole finite complex plane, which exhaust the set of all entire functions.
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Title
On unitary operators in weighted spaces $A^2_\omega(\mathbb{C})$ of entire functions
S. G. Rafayelyan and A. M. Jerbashian, On unitary operators in weighted spaces $A^2_\omega(\mathbb{C})$ of entire functions, Methods Funct. Anal. Topology 14
(2008), no. 4, 380-385.
BibTex
@article {MFAT417,
AUTHOR = {Rafayelyan, S. G. and Jerbashian, A. M.},
TITLE = {On unitary operators in weighted spaces $A^2_\omega(\mathbb{C})$ of entire functions},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {4},
PAGES = {380-385},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=417},
}