Integral Equations and Operator Theory

, Volume 12, Issue 6, pp 757–812

On Hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy

Authors

  • Harry Dym
    • Department of Theoretical MathematicsThe Weizmann Institute of Science
Article

DOI: 10.1007/BF01196878

Cite this article as:
Dym, H. Integr equ oper theory (1989) 12: 757. doi:10.1007/BF01196878

Abstract

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.

Copyright information

© Birkhäuser Verlag 1989