Recovery of the m-function from spectral data for generalized Sturm-Liouville problems

Authors:
Paul A. Binding;Patrick J. Browne;Bruce A. Watson
Affiliations:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alta., Canada T2N 1N4;Department of Computer Science, Mathematical Sciences Group, University of Saskatchewan, Sask., Saskatchewan, Canada S7N 5E6;School of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa
Venue:
Journal of Computational and Applied Mathematics - Special issue: On the occasion of the eightieth birthday of prof. W.M. Everitt
Year:
2004

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Abstract

The Sturm-Liouville problem -y''+qy=λy, y(0) cosα = y'(0) sin α, (y'/y)(1) = h(λ)/g(λ) is studied, where h and g are real polynomials. Generalized norming constants pnk associated with eigenvalues Λn are defined and formulae are given for recovering the m-function from these constants. This leads to a uniqueness theorem for the associated inverse problem.