Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (5): 947-955.

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On Rank Invariance of Generalized Loewner Matrices Generated by Stieltjes Function

Song Yanping1,2, Tang Jinbo1, Hu Yongjian1   

  1. 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

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

CLC Number: 

  • O241.3
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