K. P. Isaev, A. V. Lutsenko, R. S. Yulmukhametov, “Generating functions for bases in Hilbert spaces of entire functions”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2017, Volume 142,Pages <nobr>73

Generating functions for bases in Hilbert spaces of entire functions

K. P. Isaev^ab, A. V. Lutsenko^b, R. S. Yulmukhametov^ab

^a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
^b Bashkir State University, Ufa

Abstract: We prove that unconditional bases in a functional Hilbert space $H$ have a generating function if and only if the space $H$ is stable. Necessary and sufficient conditions for the stability of spaces adjoint to weighted spaces on an interval are obtained.

Keywords: Hilbert space, entire function, reproducing kernel, unconditional base.

UDC: 517.53

MSC: 30H20, 46E22