For the special type of weight functions on circular arc we study the asymptotic behavior of the Christoffel kernel off the arc and of the Christoffel function inside the arc. We prove Totik's conjecture for the Christoffel function corresponding to such weight functions.
On polynomials orthogonal on a circular arc
✍ Scribed by Gradimir V. Milovanović; Predrag M. Rajković
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 712 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0377-0427
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📜 SIMILAR VOLUMES
Orthogonal polynomials theory on a circular arc was apparently first developed by N. I. Akhiezer, who announced his asymptotic formulas for orthogonal polynomials on and off the support of orthogonality measure in a short note in Doklady AN SSSR. We present here a rigorous exposition of Akhiezer's r
Starting from the Delsarte Genin (DG) mapping of the symmetric orthogonal polynomials on an interval (OPI) we construct a one-parameter family of polynomials orthogonal on the unit circle (OPC). The value of the parameter defines the arc on the circle where the weight function vanishes. Some explici