Zero Location for Nonstandard Orthogonal Polynomials
โ Scribed by A.J. Duran; E.B. Saff
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 117 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0021-9045
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๐ SIMILAR VOLUMES
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
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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