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

TitleComplete systems of Bessel and inversed Bessel polynomials in spaces of holomorphic functions
Publication TypeJournal Article
Year of Publication1997
AuthorsPaneva-Konovska J
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume89
IssueLivre 1 - Mathématiques et Mecanique
Pagination79-88
ISSN0205-0808
KeywordsBessel polynomials, complete systems, 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 $K$.

1991/95 MSC

30B60, 33D25, 41A58

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