%0 DATA
%A Robert, Marlow
%D 2018
%T Spectral analysis: theory and numerical results
%U https://repository.lboro.ac.uk/articles/Spectral_analysis_theory_and_numerical_results/9384722
%2 https://repository.lboro.ac.uk/ndownloader/files/16997615
%K untagged
%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 Rayleighâ€“Ritz Approximation technique is then used to
estimate the eigenvalues.