Asymptotics for orthogonal polynomials off the circle. Issue 1 (16th May 2004) - Khaldi, R.; Benzine, R.
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.