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Zeros of polynomials orthogonal over regular N-gons

✍ Scribed by V. Maymeskul; E.B. Saff

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
173 KB
Volume
122
Category
Article
ISSN
0021-9045

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✦ Synopsis

We investigate the location of zeros of Bergman polynomials (orthogonal polynomials with respect to area measure) for regular N-gons in the plane. In particular, we prove two conjectures posed by Eiermann and Stahl. Furthermore, we give some consequences regarding the asymptotic behavior of such Bergman polynomials.

πŸ“œ SIMILAR VOLUMES

Zeros and Critical Points of Sobolev Ort
Zeros and Critical Points of Sobolev Orthogonal Polynomials
✍ W. Gautschi; A.B.J. Kuijlaars πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 340 KB

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