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
✦ LIBER ✦
Zero Location and nth Root Asymptotics of Sobolev Orthogonal Polynomials
✍ Scribed by G López Lagomasino; H Pijeira Cabrera
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 340 KB
- Volume
- 99
- Category
- Article
- ISSN
- 0021-9045
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Let f (z)=a 0 , 0 (z)+a 1 , 1 (z)+ } } } +a n , n (z) be a polynomial of degree n, given as an orthogonal expansion with real coefficients. We study the location of the zeros of f relative to an interval and in terms of some of the coefficients. Our main theorem generalizes or refines results due to