Infinite Jacobi matrices with unbounded entries: Asymptotics of eigenvalues and the transformation operator approach

被引：28

作者：

Janas, J

Naboko, S

机构：

[1] Polish Acad Sci, Inst Math, PL-31027 Krakow, Poland

[2] St Petersburg State Univ, Inst Phys, Dept Math Phys, St Petersburg 198904, Russia

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2004年 / 36卷 / 02期

关键词：

unbounded Jacobi operator; asymptotics of eigenvalues; transformation operator; successive diagonalization;

D O I：

10.1137/S0036141002406072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the exact asymptotics of eigenvalues lambda(n)(J), n-->infinity, of a class of unbounded self-adjoint Jacobi matrices J with discrete spectrum are given. Their calculation is based on a successive diagonalization approach-a new version of the classical transformation operator method. The approximations of the transformation operator are constructed step by step using a successive diagonalization procedure, which results in higher order approximations of the lambda(n)(J).

引用

页码：643 / 658

页数：16