The band method and inverse problems for orthogonal matrix functions of Szegő–Kreǐn type

A band method approach for solving inverse problems for certain orthogonal functions is developed. The inverse theorems for Szegő–Kreǐn matrix polynomials and for Kreǐn orthogonal entire matrix functions are obtained as corollaries of the band method results. Other examples, including a non-stationary variant of the Szegő–Kreǐn theorem, are presented to illustrate the scope of the abstract theorems.