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 $$(1-4zw{)}^{-1/2}exp\{\frac{1-(1-4zw{)}^{1/2}}{2z}\}=\sum _{n=0}^{\mathrm{\infty }}{B}_n(z)w^n\text{, }|4zw|<1$$ 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 $K=\{k_n{\}}_{n=0}^{\mathrm{\infty }}$ be an increasing sequence of non-negative integers. Sufficient conditions for the completeness of the systems $\{B_{k_n}(z){\}}_{n=0}^{\mathrm{\infty }}$ and $\{{\tilde{B}}_{k_n}(z){\}}_{n=0}^{\mathrm{\infty }}$ in spaces of holomorphic functions are given in terms of the density of the sequence $K$.