Complete systems of Tricomi functions in spaces of holomorphic functions

TitleComplete systems of Tricomi functions in spaces of holomorphic functions
Publication TypeJournal Article
Year of Publication1999
AuthorsRusev P
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume88
IssueLivre 3
Pagination401-407
ISSN0205-0808
Abstract

Let $\Psi(a,c;z)$ be the main branch of Tricomi confluent hypergeometric function with parameters $a,c$ and $G$ be an arbitrary simply connected subregion of the complex plane cut along the real non-positive semiaxis. It is proved that a system of the kind

\[\big\{\Psi(n + \lambda + \alpha + 1, \alpha + 1; z)\big\}_{n=0}^{\infty}\]

is complete in the space of the complex functions holomorphic in $G$ provided that $\lambda$ and $\alpha$ are real and $\lambda + \alpha > -1$.

AttachmentSize
PDF icon 88-401-407.pdf135.02 KB