Ratio Asymptotics for Polynomials Orthogonal on Arcs of the Unit Circle

Research paper by D. Barrios Rolanía, G. López Lagomasino

Indexed on: 09 Jan '99Published on: 09 Jan '99Published in: Constructive Approximation

Abstract

Ratio asymptotics for orthogonal polynomials on the unit circle is characterized in terms of the existence of limn |Φn(0)| and {limn [Φn+1(0)/Φn(0)] , where $$\{\Phi_n(0)\}_{n \geq 0}$$ denotes the sequence of reflection coefficients. The limit periodic case, that is, when these limits exist for n = j mod k , j = 1, . . ., k , is also considered.