On Hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
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- Dym, H. Integr equ oper theory (1989) 12: 757. doi:10.1007/BF01196878
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Reproducing kernel space methods are used to study the truncated matrix Hamburger moment problem on the line, an associated interpolation problem and the maximum entropy solution. Enroute a number of formulas are developed for orthogonal matrix polynomials associated with a block Hankel matrix (based on the specified matrix moments for the Hamburger problem) under less restrictive conditions than positive definiteness. An analogue of a recent formula of Alpay-Gohberg and Gohberg-Lerer for the number of roots of certain associated matrix polynomials is also established.