We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form x γ e -ϕ(x) , with γ > 0, which include as particular cases the counterparts of the so-called Freud (i.e., when ϕ has a polyn
Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports
✍ Scribed by Francisco Marcellán; Juan José Moreno Balcázar
- Publisher
- Springer Netherlands
- Year
- 2006
- Tongue
- English
- Weight
- 479 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0167-8019
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Using potential theoretic methods we study the asymptotic distribution of zeros and critical points of Sobolev orthogonal polynomials, i.e., polynomials orthogonal with respect to an inner product involving derivatives. Under general assumptions it is shown that the critical points have a canonical
We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e -x 4 on R are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e -x 4 . Some numerical examp