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

Open Mathematics (2010)

- Volume: 8, Issue: 1, page 114-128
- ISSN: 2391-5455

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topMaria Malejki. "Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l 2 by the use of finite submatrices." Open Mathematics 8.1 (2010): 114-128. <http://eudml.org/doc/269506>.

@article{MariaMalejki2010,

abstract = {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].},

author = {Maria Malejki},

journal = {Open Mathematics},

keywords = {Self-adjoint unbounded Jacobi matrix; Asymptotics; Point spectrum; Tridiagonal matrix; Eigenvalue; selfadjoint unbounded Jacobi matrix; asymptotics; point spectrum; tridiagonal matrix; eigenvalues},

language = {eng},

number = {1},

pages = {114-128},

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

url = {http://eudml.org/doc/269506},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Maria Malejki

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

JO - Open Mathematics

PY - 2010

VL - 8

IS - 1

SP - 114

EP - 128

AB - 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].

LA - eng

KW - Self-adjoint unbounded Jacobi matrix; Asymptotics; Point spectrum; Tridiagonal matrix; Eigenvalue; selfadjoint unbounded Jacobi matrix; asymptotics; point spectrum; tridiagonal matrix; eigenvalues

UR - http://eudml.org/doc/269506

ER -

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