Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators

被引：4

作者：

Dobosevych, Oles ^{[1
]}

Hryniv, Rostyslav ^{[1
,2
]}

机构：

[1] Ukrainian Catholic Univ, 2a Kozelnytska Str, UA-79026 Lvov, Ukraine

[2] Univ Rzeszow, 1 Pigonia Str, PL-35959 Rzeszow, Poland

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2021年 / 93卷 / 02期

关键词：

Operators; Rank-one perturbations; Non-simple eigenvalues; Eigenvalue asymptotics; EIGENVALUES; MATRIX; APPROXIMATIONS;

D O I：

10.1007/s00020-021-02630-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations B and discuss the inverse problem of reconstructing B from its spectrum.

引用

页数：18

共 39 条

[1] Ahlfors L.V., 1978, Complex Analysis, Vthird
[2] Finite rank perturbations and distribution theory
Albeverio, S
Kurasov, P
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (04) : 1151 - 1161
[3] Albeverio S, 2005, INTEGR EQUAT OPER TH, V52, P455, DOI 10.1007/s00020-003-1284-2
[4] Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
Albeverio, S
Koshmanenko, V
[J]. POTENTIAL ANALYSIS, 1999, 11 (03) : 279 - 287
[5] On approximations of rank one H-2-perturbations
Albeverio, S
Koshmanenko, V
Kurasov, P
Nizhnik, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (05) : 1443 - 1452
[6] Rank one perturbations of not semibounded operators
Albeverio, S
Kurasov, P
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1997, 27 (04) : 379 - 400
[7] Rank one perturbations, approximations, and selfadjoint extensions
Albeverio, S
Kurasov, P
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (01) : 152 - 169
[8] Albeverio S., 2005, Solvable Models in Quantum Mechanics, Vsecond
[9] Albeverio S., 2000, Singular Perturbations of Differential Operators Lecture Note Series, DOI [10.1017/CBO9780511758904, DOI 10.1017/CBO9780511758904]
[10] [Anonymous], 1976, GRUNDLEHREN MATHEMAT

← 1 2 3 4 →