Geodesic
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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {142},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_142_a5/}
}
TY  - JOUR
AU  - K. P. Isaev
AU  - A. V. Lutsenko
AU  - R. S. Yulmukhametov
TI  - Generating functions for bases in Hilbert spaces of entire functions
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2017
SP  - 73
EP  - 80
VL  - 142
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2017_142_a5/
LA  - ru
ID  - INTO_2017_142_a5
ER  - 
%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
%I mathdoc
%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/