Spectral analysis: theory and numerical results
MarlowRobert
2018
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.