On the operator equation AX - XB plus XDX = C

被引：0

作者：

Bezai, A. ^{[1
]}

Lombarkia, F. ^{[1
]}

机构：

[1] Univ Batna 2, Fac Math & Informat, Dept Math, Lab Math Tech LTM, Batna 05078, Algeria

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2023年 / 72卷 / 08期

关键词：

Ricatti operator equation; Lyapunov operator equation; Generalized Drazin inverse; Inner inverse; Cauchy problems; GENERALIZED DRAZIN INVERSE;

D O I：

10.1007/s12215-023-00887-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By application of the generalized Drazin inverse a method for solving Riccati and Lyapunov operator equations in Hilbert space are given. Results are applied to the problem of finding general solutions for Cauchy problems for Riccati and Lyapunov operator differential equations.

引用

页码：4179 / 4187

页数：9

共 50 条

[1] On the solution of the matrix equation AX plus XB=C
Rutherford, DE
PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1932, 35 (1/5): : 54 - 59
[2] Concerning the matrix equation AX plus XB=C
Weitzenbock, R
PROCEEDINGS OF THE KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN TE AMSTERDAM, 1932, 35 (1/5): : 60 - 61
[3] Solving the Operator Equation AX - XB = C with Closed A and B
Djordjevic, Bogdan D.
Dincic, Nebojsa C.
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2018, 90 (05)
[4] THE OPERATOR EQUATION AX-XB = C WITH NORMAL A AND B
SCHWEINSBERG, A
PACIFIC JOURNAL OF MATHEMATICS, 1982, 102 (02) : 447 - 453
[5] OPERATOR EQUATION AX+XB=Q
GOLDSTEIN, JA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 70 (01) : 31 - 34
[6] 关于矩阵方程XDX+AX+XB+C=0
王肇华
安徽大学学报(自然科学版), 1985, (03) : 13 - 17
[7] The Quaternionic Equation ax + xb = c
Jacques Helmstetter
Advances in Applied Clifford Algebras, 2012, 22 : 1055 - 1059
[8] MATRIX EQUATION AX + XB = C
KUCERA, V
SIAM JOURNAL ON APPLIED MATHEMATICS, 1974, 26 (01) : 15 - 25
[9] The operator equation AX-XB = C, admissibility, and asymptotic behavior of differential equations
Phong, VQ
Schuler, E
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (02) : 394 - 419
[10] SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX+XB=Y
ARENDT, W
RABIGER, F
SOUROUR, A
QUARTERLY JOURNAL OF MATHEMATICS, 1994, 45 (178): : 133 - 149

← 1 2 3 4 5 →