On the Trace Approximation Problem for Truncated Toeplitz Operators and Matrices

The paper is devoted to the problem of approximation of the traces of products of truncated Toeplitz operators and matrices generated by integrable real symmetric functions defined on the real line (resp. on the unit circle), and estimation of the corresponding errors. These approximations and the corresponding error bounds are of importance in the statistical analysis of continuous-and discrete-time stationary processes (asymptotic distributions and large deviations of Toeplitz type quadratic functionals and forms, parametric and nonparametric estimation, etc.) We review and summarize the known results concerning the trace approximation problem and prove some new results.