Complete systems of Bessel and inversed Bessel polynomials in spaces of holomorphic functions

Abstract

Let $B_{n}(z),n = 0,1,...,$ be the Bessel polynomials generated by \[(1 - 4zw)^{-1/2}exp\bigg\{ \frac{1 - (1 - 4zw)^{1/2}}{2z}\bigg\}=\sum\limits_{n=0}^{\infty}B_{n}(z)w^{n}\textrm{, } |4zw| < 1\] and the functions $\tilde{B}_{n}(z)$ be defined by the relations \[\tilde{B}_{n}(z)=4^{-n}z^{n}B_{n}(1/z)exp(-z/2).\] Let $K = \{k_{n}\}_{n=0}^{\infty}$ be an increasing sequence of non-negative integers. Sufficient conditions for the completeness of the systems $\{B_{k_{n}}(z)\}_{n=0}^{\infty}$ and $\{\tilde{B}_{k_{n}}(z)\}_{n=0}^{\infty}$ in spaces of holomorphic functions are given in terms of the density of the sequence $K$.