Asymptotics for orthogonal polynomials off the circle. Issue 1 (16th May 2004)

• Record Type: Journal Article
• Authors: Khaldi, R.; Benzine, R.
• Is Part Of: Journal of applied mathematics. Volume 2004:Issue 1(2004)
• Page Start: 37
• Page End: 53
• Publication Date: 2004-05-16
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/S1110757X04304092
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We study the strong asymptotics of orthogonal polynomials with respect to a measure of the type d μ / 2 π + ∑ j = 1 ∞ A j δ ( z − z k ), where μ is a positive measure on the unit circle Γ satisfying the Szegö condition and { z j } j = 1 ∞ are fixed points outside Γ . The masses { A j } j = 1 ∞ are positive numbers such that ∑ j = 1 ∞ A j < + ∞ . Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.