Article

# Limit points of eigenvalues of truncated unbounded tridiagonal operators

• ##### E. Petropoulou
Central European Journal of Mathematics (Impact Factor: 0.41). 05/2007; 5(2):335-344. DOI: 10.2478/s11533-007-0009-1

ABSTRACT Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e

n
}

n=1

, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T

N
. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.

0 Bookmarks
·
69 Views
• Source
##### Article: Self-adjointness of unbounded tridiagonal operators and spectra of their finite truncations
[Hide abstract]
ABSTRACT: This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient conditions given in both cases improve and generalize previously known results. It turns out that, not only self-adjointness helps to study limit points of eigenvalues of truncated operators, but the analysis of such limit points is a key help to prove self-adjointness. Several examples show the advantages of these new results compared with previous ones. Besides, an application to the theory of continued fractions is pointed out.
Journal of Mathematical Analysis and Applications 02/2014; 420(1). · 1.05 Impact Factor
• Source
##### Article: Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials
[Hide abstract]
ABSTRACT: Sequences {pn}n=0∞ of polynomials, orthogonal with respect to signed measures, are associated with a class of differential equations including the Mathieu, Lamé and Whittaker–Hill equation. It is shown that the zeros of pn form sequences which converge to the eigenvalues of the corresponding differential equations. Moreover, interlacing properties of the zeros of pn are found. Applications to the numerical treatment of eigenvalue problems are given.
Journal of Computational and Applied Mathematics 01/2008; 213(2):488-500. · 0.99 Impact Factor
• Source
##### Article: On the spectral measure of a class of orthogonal polynomials
Journal of Computational and Applied Mathematics 01/2001; 133(1):688-689. · 0.99 Impact Factor