Reduction Techniques: From Nonstationary to Stationary and Vice Versa

Abstract

This chapter presents the reduction technique that will allow us to convert nonstationary interpolation problems into stationary ones. This technique is based on a transformation (and its inverse) which maps a doubly infinite operator matrix $F{\text{ = }}\left( {{f_{j,k}}} \right)_{j,k{\text{ = - }}\infty }^\infty$ into a doubly infinite block Laurent matrix $\hat F = \left( {\left[ F \right]_{j - k} } \right)_{j,k = - \infty }^\infty$ where [F]_n is the matrix which one obtains from F if all (operator) entries in F are set to zero except those on the n-th diagonal which are left unchanged.