𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The extremal zeros of a perturbed orthogonal polynomials system

✍ Scribed by Elie Leopold


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
844 KB
Volume
98
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis


The purpose of this paper is to study how the exlremal zeros of a family of orthogonal polynomials evolve when we perturb the coefficient of the recurrence relation defining the family. To this end we shall compare the extremal zeros with the corresponding zeros in the perturbed ease.


πŸ“œ SIMILAR VOLUMES


Representations for the extreme zeros of
✍ Erik A. van Doorn; Nicky D. van Foreest; Alexander I. Zeifman πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 378 KB

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the de

Zeros of orthogonal polynomials on the r
✍ Sergey A Denisov; Barry Simon πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 144 KB

Let p n Γ°xÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppΓ°dmÞ; we show there is a d40 so that for all n; either p n or p nΓΎ1 has no zeros in Γ°E Γ€ d; E ΓΎ dÞ: If E is an isolated point of suppΓ°mÞ; we show there is a d so that for all n; either p n or p nΓΎ