关键词: 矩阵测度, Hamburger矩阵矩量问题, 广义Akhiezer矩阵插值,  N -极端矩阵测度, Riesz定理, 有限阶解

Abstract:

In this paper we describe solutions ρ of finite order to a completely indeterminate Hamburger matrix moment problem with moments
{ν_m}₀^∞( C^q×q: ν_m=∫_-∞^∞x^mdρ(x), m=0,1, …, i.e., those solutions ρ for which the linear space P of C^q ×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