Solving the Operator Equation AX - XB = C with Closed A and B

被引：0

作者：

Djordjevic, Bogdan D. ^{[1
]}

Dincic, Nebojsa C. ^{[1
]}

机构：

[1] Univ Nis, Fac Sci & Math, Dept Math, POB 224, Nish 18000, Serbia

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2018年 / 90卷 / 05期

关键词：

Sylvester equation; Closed operator; Sturm-Liouville problem;

D O I：

10.1007/s00020-018-2473-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the operator equation , where A and B are closed operators whose point spectra intersect. We obtain sufficient conditions for the existence of solutions and provide a way of constructing them. As a corollary, we obtain a result that gives us new insight on the matrix equations of the form , where A and B share non-zero eigenvalues. Afterwards, we illustrate our results on Sturm-Liouville operators.

引用

页数：25