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

• Autorzy: Maria Malejki
• Języki publikacji: EN

Abstrakty

EN

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(ℕ) 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 → ∞) 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 × n; where N = max{k ∈ ℕ: k ≤ rn} and r ∈ (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].

Słowa kluczowe

EN

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

Kategorie tematyczne

• 15A18: Eigenvalues, singular values, and eigenvectors
• 47B25: Symmetric and selfadjoint operators (unbounded)
• 47B36: Jacobi (tridiagonal) operators (matrices) and generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 114-128

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Maria Malejki

• AGH University of Science and Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0064-x