Bounds and inequalities for arbitrary orthogonal polynomials on finite intervals
It seems that the main goal of this paper is to improve results of the author's previous paper [J. Approximation Theory 73, No. 3, 303-335 (1993; Zbl 0780.42017)] concerning bounds and inequalities for the orthogonal polynomials with respect to the measure \(d\alpha\), where \(\alpha\) is a nondecreasing function on \([-1,1]\) with infinitely many points of increase such that all moments of \(d\alpha\) are finite. The key tool for this improvement is the observation that for any measure \(d\alpha\) supported in \([-1,1]\) there exists a positive \(\delta< 2\) such that \[ \textstyle{\inf_{\Omega\text{ (Lebesgue measurable) }\subset [- 1, 1],|\Omega|= \delta}}\Biggl\{\int_ \Omega d\alpha(x)\Biggl/\int_{[- 1,1]} d\alpha(x)\Biggr\}> 0. \] {}.
Lagrange and Hermite-Fejér interpolation polynomials
scientific article; zbMATH DE number 756616
scientific article