Asymptotic formulas for determinants of a special class of toeplitz + hankel matrices

Abstract

We compute the asymptotics of the determinants of certain n × n Toeplitz + Hankel matrices Tn(a)+Hn(b) as n→∞with symbols of Fisher-Hartwig type. More specifically we consider the case where a has zeros and poles and where b is related to a in specific ways. Previous results of Deift, Its and Krasovsky dealt with the case where a is even. We are generalizing this in a mild way to certain non-even symbols.