Generating Functions for Bases in Hilbert Spaces of Entire Functions


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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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K. Isaev

Institute of Mathematics with Computer Center of the Russian Academy of Sciences; Bashkir State University

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Email: orbit81@list.ru
俄罗斯联邦, Ufa; Ufa

A. Lutsenko

Bashkir State University

Email: orbit81@list.ru
俄罗斯联邦, Ufa

R. Yulmukhametov

Institute of Mathematics with Computer Center of the Russian Academy of Sciences; Bashkir State University

Email: orbit81@list.ru
俄罗斯联邦, Ufa; Ufa

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