| 完全不确定Hamburger矩阵矩量问题的有限阶解 |
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| 引用本文： | 陈公宁,秦建国. 完全不确定Hamburger矩阵矩量问题的有限阶解[J]. 数学物理学报(A辑), 2010, 30(3): 577-583 |
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| 作者姓名： | 陈公宁 秦建国 |
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| 作者单位： | 陈公宁(北京师范大学数学科学学院,北京,100875);秦建国(郑州轻工业学院数学与信息科学系,郑州,450002) |
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| 摘 要： | 该文描述带有矩量序列{v_m}_0~∞■C~(q×q)的完全不确定Hamburger矩阵矩量问题:v_m=integral from n=-∞to∞x~m dρ(x),m=0,1,…的有限阶解,即该问题的那些解ρ,使得C~(q×q)-值多项式的线性空间P在对应的空间L~2(R,dρ/E(x))内稠密,这里E(x)为在实轴R上取正值的某个数值多项式.作为预备知识,作者考虑所谓广义Akhiezer插值的矩阵变种与它的相关矩阵矩量问题之间的一种关系.
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| 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 |
| 收稿时间： | 2007-12-11 |
| 修稿时间： | 2009-07-06 |
Solutions of Finite Order to a Completely Indeterminate Hamburger Matrix Moment Problem |
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| CHEN Gong-Ning,QIN Jian-Guo. Solutions of Finite Order to a Completely Indeterminate Hamburger Matrix Moment Problem[J]. Acta Mathematica Scientia, 2010, 30(3): 577-583 |
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| Authors: | CHEN Gong-Ning QIN Jian-Guo |
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| Affiliation: | 1.School of Mathematical Sciences, Beijing Normal University, Beijing 100875;2.Department of Mathematics and Information Science, Zhengzhou Light Industry Institute, Zhengzhou 450002 |
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| Abstract: | In this paper we describe solutions ρ of finite order to a completely indeterminate Hamburger matrix moment problem with moments{νm}0∞( Cq×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. |
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| Keywords: | Matrix measurezz Hamburger matrix moment problemzz Generalized Akhiezer matrix interpolationzz N-extremal matrix measurezz Riesz’s theoremzz Solution of finite orderzz |
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