Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 577-583.

• Articles •     Next Articles

Solutions of Finite Order to a Completely Indeterminate Hamburger Matrix Moment Problem

 CHEN Gong-Ning, QIN Jian-Guo   

  1. 1.School of Mathematical Sciences, Beijing Normal University, Beijing 100875;
    2.Department of Mathematics and Information Science, Zhengzhou Light Industry Institute, Zhengzhou 450002
  • Received:2007-12-11 Revised:2009-07-06 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    国家自然科学基金(10271018)资助.

Abstract:

In this paper we describe solutions ρ of finite order to a completely indeterminate Hamburger matrix moment problem with moments
{νm}0Cq×q: νm=∫-∞xmdρ(x), m=0,1, …, i.e., those solutions ρ for which the linear space P of Cq ×q -valued polynomials is dense in the corresponding L2(R, dρ / E(x) for some scalar polynomial E(x) positive on the real line R. As preliminaries we consider a certain connection of a matrix version of the so-called generalized Akhiezer interpolation with its related matrix moment problem.

Key words: Matrix measure, Hamburger matrix moment problem, Generalized Akhiezer matrix interpolation, N-extremal matrix measure, Riesz’s theorem, Solution of finite order

CLC Number: 

  • 42C05
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