Forward and inverse spectral theory of Sturm-Liouville operators with transmission conditions
Date
2017
Authors
Bartels, Casey Ann
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Abstract
ForwardandinversespectralproblemsconcerningSturm-Liouvilleoperatorswithoutdiscontinuitieshavebeenstudiedextensively. Bycomparison,therehasbeenlimitedworktacklingthecase where the eigenfunctions have discontinuities at interior points, a case which appears naturally in physical applications. We refer to such discontinuity conditions as transmission conditions. We consider Sturm-Liouville problems with transmission conditions rationally dependent on the spectral parameter. We show that our problem admits geometrically double eigenvalues, necessitating a new analysis. We develop the forward theory associated with this problem and also consider a related inverse problem. In particular, we prove a uniqueness result analogous to that of H. Hochstadt on the determination of the potential from two sequences of eigenvalues. In addition, we consider the problem of extending Sturm’s oscillation theorem, regarding the number of zeroes of eigenfunctions, from the classical setting to discontinuous problems with general constant coefficient transmission conditions
Description
Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, School of Mathematics, 2017.
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Citation
Bartels, Casy Ann (2017) Forward and inverse spectral theoryof Sturm-Liouville operators with transmission conditions, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23751>