ETD Collection

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2012 - 20153

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    Spectral analysis of self-adjoint second order differential operators
    (2015-03) Boshego, Norman
    The primary purpose of this study is to investigate the asymptotic distribution of the eigenvalues of self-adjoint second order di erential operators. We rst analyse the problem where the functions g and h are equal to zero. To improve on the terms of the eigenvalue problem for g; h = 0, we consider the eigenvalue problem for general functions g and h. Here we calculate explicitly the rst four terms of the eigenvalue asymptotics problem.
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    Forward and inverse problem of Hermitian systems in C2.
    (2015-05-06) Roth, Thomas
    In this thesis, the forward and inverse Spectral Theory for first order Hermitian systems with complex potentials and periodic boundary conditions are studied. The aim of this work is to prove two inverse periodicity Theorems and two uniqueness results for determinants of quasiperiodic boundary value problems.
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    Spectral theory of self-adjoint higher order differential operators with eigenvalue parameter dependent boundary conditions
    (2012-09-05) Zinsou, Bertin
    We consider on the interval [0; a], rstly fourth-order di erential operators with eigenvalue parameter dependent boundary conditions and secondly a sixth-order di erential operator with eigenvalue parameter dependent boundary conditions. We associate to each of these problems a quadratic operator pencil with self-adjoint operators. We investigate the spectral proprieties of these problems, the location of the eigenvalues and we explicitly derive the rst four terms of the eigenvalue asymptotics.