3. Electronic Theses and Dissertations (ETDs) - All submissions

Permanent URI for this communityhttps://wiredspace.wits.ac.za/handle/10539/45

Browse

Filters

20171

Settings

Author: search.filters.author.Bartels, Casey AnnSubject: search.filters.subject.Spectral theory (Mathematics)

Search Results

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Forward and inverse spectral theory of Sturm-Liouville operators with transmission conditions
    (2017) Bartels, Casey Ann
    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
Copyright Ownership Is Guided By The University's

Intellectual Property policy

Students submitting a Thesis or Dissertation must be aware of current copyright issues. Both for the protection of your original work as well as the protection of another's copyrighted work, you should follow all current copyright law.