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Spectral analysis: theory and numerical results

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thesis
posted on 20.11.2018, 09:27 by Robert Marlow
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.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© Robert Marlow

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2005

Notes

A Master's Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Master of Philosophy at Loughborough University.

Language

en

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