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

ЗаглавиеComplete systems of Bessel and inversed Bessel polynomials in spaces of holomorphic functions
Вид публикацияJournal Article
Година на публикуване1997
АвториPaneva-Konovska J
СписаниеAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Том89
IssueLivre 1 - Mathématiques et Mecanique
Pagination79-88
ISSN0205-0808
ключови думиBessel polynomials, complete systems, holomorphic functions
Резюме

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 $K$.

1991/95 MSC

30B60, 33D25, 41A58

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