Asymptotic formulas for determinants of a special class of Toeplitz + Hankel matrices

Original · EN

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.