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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 2, 1995, pp. 327–345
DOI: 10.4171/ZAA/677

Published online: 1995-06-30

Variational Bounds to Eigenvalues of Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum

S. Zimmermann[1] and U. Mertins[2]

(1) Technische Universität Clausthal, Clausthal-Zellerfeld, Germany
(2) Technische Universität Clausthal, Clausthal-Zellerfeld, Germany

In the present paper a method by Lehmann-Maehly and Goerisch is extended to self-adjoint eigenvalue problems with arbitrary essential spectrum. This extension is obtained by consequently making use of the local character of the method. In this way, upper and lower bounds to all isolated eigenvalues are derived. In our proofs, the close relationship to Wielandt’s inverse iteration becomes quite obvious.

Keywords: Eigenvalue problems, variational methods, upper and lower bounds to eigenvalues

Zimmermann S., Mertins U.: Variational Bounds to Eigenvalues of Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum. Z. Anal. Anwend. 14 (1995), 327-345. doi: 10.4171/ZAA/677