An Interpolation Problem for Hilbert-Schmidt Operator-Valued Stationary Processes

Abstract

The paper contains a solution of the following interpolation problem for Hilbert-Schmidt operator-valued stationary processes on the real line: Assume that the values of the process on the integers are known. Determine the best linear approximation of an unknown value on the basis of the known values and compute the approximation error. Our results generalize previous results of Yaglom and Salehi for univariate and $q$-variate processes, respectively.