Generating functions for bases in Hilbert spaces of entire functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 73-80
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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.
Keywords:
Hilbert space, entire function, reproducing kernel, unconditional base.
@article{INTO_2017_142_a5,
author = {K. P. Isaev and A. V. Lutsenko and R. S. Yulmukhametov},
title = {Generating functions for bases in {Hilbert} spaces of entire functions},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {73--80},
year = {2017},
volume = {142},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2017_142_a5/}
}
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%0 Journal Article %A K. P. Isaev %A A. V. Lutsenko %A R. S. Yulmukhametov %T Generating functions for bases in Hilbert spaces of entire functions %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2017 %P 73-80 %V 142 %U http://geodesic.mathdoc.fr/item/INTO_2017_142_a5/ %G ru %F INTO_2017_142_a5
K. P. Isaev; A. V. Lutsenko; R. S. Yulmukhametov. Generating functions for bases in Hilbert spaces of entire functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 142 (2017), pp. 73-80. http://geodesic.mathdoc.fr/item/INTO_2017_142_a5/