Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 142, Pages 73–80 (Mi into254)  
Generating functions for bases in Hilbert spaces of entire functions

K. P. Isaevab, A. V. Lutsenkob, R. S. Yulmukhametovab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Bashkir State University, Ufa
Full-text PDF (183 kB)
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.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 6, Pages 718–726
DOI: https://doi.org/10.1007/s10958-019-04457-w
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30H20, 46E22
Language: Russian
Citation: K. P. Isaev, A. V. Lutsenko, R. S. Yulmukhametov, “Generating functions for bases in Hilbert spaces of entire functions”, Complex analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 142, VINITI, M., 2017, 73–80; Journal of Mathematical Sciences, 241:6 (2019), 718–726
Citation in format AMSBIB
\Bibitem{IsaLutYul17}
\by K.~P.~Isaev, A.~V.~Lutsenko, R.~S.~Yulmukhametov
\paper Generating functions for bases in Hilbert spaces of entire functions
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 142
\pages 73--80
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801350}
\zmath{https://zbmath.org/?q=an:1426.30045}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 6
\pages 718--726
\crossref{https://doi.org/10.1007/s10958-019-04457-w}
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