Asymptotics for orthogonal polynomials off the circle. Issue 1 (16th May 2004) - Khaldi, R.
Abstract : We study the strong asymptotics of orthogonal polynomials with respect to a measure of the typed μ / 2 π + ∑ j = 1 ∞ A j δ ( z − z k ), whereμ is a positive measure on the unit circleΓ satisfying the Szegö condition and{ z j } j = 1 ∞ are fixed points outsideΓ . 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.