The Partial Trigonometric Moment Problem on an Interval: The Matrix Case
As was proved by Akhiezer and Krein, the partial trigonometric moment problem on an interval has solutions if and only if two Toeplitz matrices built from the data are nonnegative. In this work, set in the matrix case, we exhibit relationships between the orthogonal polynomials associated to these matrices. This allows us to solve the matrix version of the partial trigonometric moment problem on an interval in the nondegenerate case.
D. Alpay and Ph. Loubaton, The partial trigonometric moment problem on an interval: the matrix case. In Linear Algebra and its Applications, Vol. 225 (1995) 141-161.