Stieltjes函数生成的广义Loewner矩阵的秩不变性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 947-955.

Stieltjes函数生成的广义Loewner矩阵的秩不变性

宋艳萍^1,2, 唐金波¹, 胡永建¹

1 北京师范大学数学科学学院北京 100875;
2 新疆农业大学数理学院乌鲁木齐 830052

收稿日期:2014-03-25 修回日期:2015-04-25 出版日期:2015-10-25 发布日期:2015-10-25
作者简介:宋艳萍,ypsong@mail.bnu.edu.cn;唐金波,bojintang@126.com;胡永建,yongjian@bnu.edu.cn
基金资助:
国家自然科学基金(11071017,11271045)和中央高校基本科研业务费资助

On Rank Invariance of Generalized Loewner Matrices Generated by Stieltjes Function

Song Yanping^1,2, Tang Jinbo¹, Hu Yongjian¹

1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875;
2 The College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi 830052

Received:2014-03-25 Revised:2015-04-25 Online:2015-10-25 Published:2015-10-25

摘要/Abstract

摘要：

研究由Stieltjes函数生成的两类广义Loewner矩阵的秩不变性,证明了由同一Stieltjes函数生成的第一类同型的广义Loewner矩阵的秩是相等的,而生成的第二类同型的广义Loewner矩阵的秩相等或者相差1.

关键词: Stieltjes函数, 广义Loewner矩阵, Hankel矩阵, 秩不变, Stieltjes矩量问题

Abstract:

In this paper we study the statements on rank invariance of generalized Loewner matrices of two types generated by the values of a given Stieltjes function. We show that the ranks of such matrices of the first type of the same size are equal, while the ranks of such matrices of the second type with the same size are either equal or differ with difference one.

Key words: Stieltjes function, Generalized Loewner matrix, Hankel matrix, Rank invariance, Stieltjes moment problem

中图分类号:

O241.3

宋艳萍, 唐金波, 胡永建. Stieltjes函数生成的广义Loewner矩阵的秩不变性[J]. 数学物理学报, 2015, 35(5): 947-955.

Song Yanping, Tang Jinbo, Hu Yongjian. On Rank Invariance of Generalized Loewner Matrices Generated by Stieltjes Function[J]. Acta mathematica scientia,Series A, 2015, 35(5): 947-955.

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