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

  • Harry Dym
Article

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.

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Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Harry Dym
    • 1
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceIsrael

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