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A two-parameter eigenvalue problem involving complex potentials

Published online by Cambridge University Press:  14 November 2011

M. Faierman
M. Faierman
Affiliation:
Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
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Synopsis

We consider a two-parameter system of ordinary differential equations of the second order involving complex potentials and show that, unlike the case of real potentials, the eigenfunctions of the system do not necessarily form a complete set in the usual Hilbert space associated with the problem. We also give a necessary and sufficient condition for the eigenfunctions to be complete. Finally, we establish some results concerning the eigenvalues of the system.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 177 - 191
Copyright
Copyright © Royal Society of Edinburgh 1990

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