Abstract:
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 $\sigma(A)\in (0,41,\quad 0,5]$.
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