Generating Functions for Bases in Hilbert Spaces of Entire Functions

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.

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019-09, Vol.241 (6), p.718-726
Main Authors: Isaev, K. P., Lutsenko, A. V., Yulmukhametov, R. S.
Format: Article
Language:English
Subjects:
Entire functions
Functionals
Hilbert space
Mathematics
Mathematics and Statistics
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Description
Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04457-w