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

摘要

We compute the asymptotics of the determinants of certain $n\times n$Toeplitz + Hankel matrices $T_n(a)+H_n(b)$ as $n\to\infty$ with symbols ofFisher-Hartwig type. More specifically we consider the case where $a$ has zerosand poles and where $b$ is related to $a$ in specific ways. Previous results ofDeift, Its and Krasovsky dealt with the case where $a$ is even. We aregeneralizing this in a mild way to certain non-even symbols.