Electron. J. Diff. Eqns., Vol. 2005(2005), No. 48, pp. 1-15.

Eigenvalue problems of Atkinson, Feller and Krein, and their mutual relationship

Hans Volkmer

It is shown that every regular Krein-Feller eigenvalue problem can be transformed to a semidefinite Sturm-Liouville problem introduced by Atkinson. This makes it possible to transfer results between the corresponding theories. In particular, Prüfer angle methods become available for Krein-Feller problems.

Submitted September 13, 2004. Published April 28, 2005.
Math Subject Classifications: 34B24, 34B09
Key Words: Sturm-Liouville problem; vibrating string; Krein-Feller eigenvalue problem; Atkinson eigenvalue problem.

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Hans Volkmer
Department of Mathematical Sciences
University of Wisconsin-Milwaukee
P. O. Box 413
Milwaukee, WI 53201 USA
email: volkmer@csd.uwm.edu

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