ACCUMULATION OF COMPLEX EIGENVALUES OF AN INDEFINITE STURM-LIOUVILLE OPERATOR WITH A SHIFTED COULOMB POTENTIAL

被引：6

作者：

Levitin, Michael ^{[1
]}

Seri, Marcello ^{[1
]}

机构：

[1] Univ Reading, Dept Math & Stat, POB 220, Reading RG6 6AX, Berks, England

来源：

OPERATORS AND MATRICES | 2016年 / 10卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Linear operator pencils; non-self-adjoint operators; Sturm-Liouville problem; Coulomb potential; complex eigenvalues; Kummer functions; DIFFERENTIAL-OPERATORS; SIMILARITY PROBLEM; SGN X;

D O I：

10.7153/oam-10-14

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm-Liouville operator A = sign(x)(-Delta+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

引用

页码：223 / 245

页数：23

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