Opuscula Mathematica
Opuscula Math. 30, no. 3 (), 311-330
Opuscula Mathematica

Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices

Abstract. The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from \(1\) to \(N\), for a Jacobi matrix \(J\) by the eigenvalues of the finite submatrix \(J_n\) of order \(pn \times pn\), where \(N = \max \{k \in \mathbb{N}: k \leq rpn\}\) and \(r \in (0,1)\) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of \(J\) in the case \(p=3\).
Keywords: symmetric unbounded Jacobi matrix, block Jacobi matrix, tridiagonal matrix, point spectrum, eigenvalue, asymptotics.
Mathematics Subject Classification: 47A75, 47B25, 47B36, 15A18.
Cite this article as:
Maria Malejki, Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices, Opuscula Math. 30, no. 3 (2010), 311-330, http://dx.doi.org/10.7494/OpMath.2010.30.3.311
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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