Asymptotic formulas for Toeplitz and Wiener-Hopf operators

For certain analytic functions f, the expression trace {f(T_n]) – f(T_n]T_n])} is computed asymptotically. Here T_n] is the finite Toeplitz matrix generated by the function . The analogous expression for Wiener-Hopf operators is also computed asymptotically. These results in turn yield information concerning the asymptotic behavior of determinants of finite Toeplitz and Wiener-Hopf operators with discontinuous generating function.