IJPAM: Volume 2, No. 4 (2002)

ON THE PROPERTIES OF ORTHOGONAL
POLYNOMIALS OVER A REGION WITH
ANALYTIC WEIGHT FUNCTION

F.G. Abdullayev$^1$, M. Küçükaslan$^2$
$^1$Dept. of Mathematics
Faculty of Arts & Science
Mersin University
33342 Mersin, TURKEY
e-mail: fabdul@mersin.edu.tr
$^2$Dept. of Mathematics
Faculty of Arts & Science
Çukurova University
Mersin, TURKEY
e-mail: mkucukaslan@mersin.edu.tr


Abstract.Let $G\subset C$ be a finite region bounded by Jordan curve $%
L:=\partial G$ and $\ h(z)>0\;$ be a weight function on $G$; $\left\{
K_{n}(z)\right\} _{n=0}^{\infty }\;$ be a orthonormal system for the pair $%
(G,h)$. In this paper, we investigate some properties of the orthonormal polynomials and we are going to find an upper bound for $\left\vert
K_{n}(z)\right\vert,\;z\in G$ in regions of the complex plane depending of geometric properties and the distance of $\ \ z\in G$ to the boundary $L$.

Received: March 3, 2002

AMS Subject Classification: 41A10, 30E10, 42A16

Key Words and Phrases: approximation by polynomials, orthogonal polynomials, quasicircle, analytic weight functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 4