%0 Thesis %A Marlow, Robert %D 2018 %T Spectral analysis: theory and numerical results %U https://repository.lboro.ac.uk/articles/thesis/Spectral_analysis_theory_and_numerical_results/9384722 %2 https://repository.lboro.ac.uk/ndownloader/files/16997615 %K untagged %K Mathematical Sciences not elsewhere classified %X This paper explains how spectral theory characterises an operator, acting on a Banach or Hilbert space, and so helps to solve an equation of that operator, or characterise its solution. Sobolev spaces are discussed, and then Spectral theory is applied to a Laplace operator with Dirichlet boundary conditions, and the eigenvalues characterised. An adapted version of the Rayleigh–Ritz Approximation technique is then used to estimate the eigenvalues. %I Loughborough University