The extremal zeros of a perturbed orthogonal polynomials system
β 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.
β¦ 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.
π SIMILAR VOLUMES
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
Let p n Γ°xΓ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppΓ°dmΓ; 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 dΓ: If E is an isolated point of suppΓ°mΓ; we show there is a d so that for all n; either p n or p nΓΎ