Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l (2) by the use of finite submatrices

作者：Malejki Maria^*

来源：Central European Journal of Mathematics, 2010, 8(1): 114-128.

DOI：10.2478/s11533-009-0064-x

• Self-adjoint unbounded Jacobi matrix
• Asymptotics
• Point spectrum
• Tridiagonal matrix
• Eigenvalue

We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l (2)(a"center dot) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n -> a) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J (n) of order n x n; where N = max{k a a"center dot: k a parts per thousand currency sign rn} and r a (0; 1) is arbitrary chosen. We apply this result to obtain an asymptotics for the eigenvalues of J. The method applied in this research is based on Volkmer's results included in [23].

• 出版日期2010-2