Article
Limit points of eigenvalues of truncated unbounded tridiagonal operators
Central European Journal of Mathematics (Impact Factor: 0.52). 05/2007; 5(2):335344. DOI: 10.2478/s1153300700091

Article: Selfadjointness of unbounded tridiagonal operators and spectra of their finite truncations
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ABSTRACT: This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its selfadjointness 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 selfadjointness helps to study limit points of eigenvalues of truncated operators, but the analysis of such limit points is a key help to prove selfadjointness. 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). · 1.12 Impact Factor 
Article: Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials
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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 04/2008; 213(2):488500. · 1.08 Impact Factor  Journal of Computational and Applied Mathematics 08/2001; 133(1):688689. · 1.08 Impact Factor
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