On~the~basis property of certain polynomial systems in spaces of entire functions of exponential type
Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 587-599.

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

A class $A$ of polynomial systems $\{a _n(z)\}_0^\infty (a_n^{(n)}(z)\equiv 1,$ $\ n\geqslant 0)$ is considered such that each polynomial $a_n(z)$, starting with $a_1(z)$, has together with its derivatives of order up to and including $(n-1)$at least one zero in the closed unit disc. It is shown that each polynomial system of the class $A$ forms a quasipower basis in the space of entire functions of exponential type less than $R$ $(R>0)$, provided $R$ does not exceed a certain absolute constant $\sigma(A)\in (0,41,\quad 0,5]$.
@article{IM2_1994_42_3_a4,
     author = {V. A. Oskolkov},
     title = {On~the~basis property of certain polynomial systems in spaces of entire functions of exponential type},
     journal = {Izvestiya. Mathematics },
     pages = {587--599},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a4/}
}
TY  - JOUR
AU  - V. A. Oskolkov
TI  - On~the~basis property of certain polynomial systems in spaces of entire functions of exponential type
JO  - Izvestiya. Mathematics 
PY  - 1994
SP  - 587
EP  - 599
VL  - 42
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a4/
LA  - en
ID  - IM2_1994_42_3_a4
ER  - 
%0 Journal Article
%A V. A. Oskolkov
%T On~the~basis property of certain polynomial systems in spaces of entire functions of exponential type
%J Izvestiya. Mathematics 
%D 1994
%P 587-599
%V 42
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a4/
%G en
%F IM2_1994_42_3_a4
V. A. Oskolkov. On~the~basis property of certain polynomial systems in spaces of entire functions of exponential type. Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 587-599. http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a4/

[1] Kazmin Yu. A., “Vozmuschennye mnogochleny Appelya i assotsiirovannye s nimi sistemy funktsii”, DAN SSSR, 282:1 (1985), 19–22 | MR

[2] Kazmin Yu. A., “O razlozheniyakh v ryady po polinomam Appelya”, Matem. zametki, 5:5 (1969), 509–520 | MR

[3] Macyntyre S. S., “An upper bound for the Whittaker constant”, London Math. Soc. J., 22 (1947), 305–311 | DOI | MR

[4] Evgrafov M. A., Interpolyatsionnaya zadacha Abelya–Goncharova, Gostekhizdat, M., 1954

[5] Banakh S., Kurs funktsionalnogo analiza, Radyanska shkola, Kiiv, 1948

[6] Markushevich A. I., “O bazise v prostranstve analiticheskikh funktsii”, Matem. sb., 17:2 (1945), 211–252 | Zbl

[7] Evgrafov M. A., “Metod blizkikh sistem v prostranstve analiticheskikh funktsii i ego primeneniya k interpolyatsii”, Tr. mosk. matem. ob-va, 5, 1956, 89–201 | MR | Zbl