Spectra of indefinite linear operator pencilsOzturk, H. M. (2019) Spectra of indefinite linear operator pencils. PhD thesis, University of Reading
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.48683/1926.00085871 Abstract/SummaryIn recent years, there has been a rapid growth of interest in spectral properties of non-self-adjoint operators and operator pencils. This thesis is concerned with indefinite self-adjoint linear pencils which lead to a special class of non-self-adjoint spectral problems. These problems are not well understood, and, in general, many sign-indefinite problems which are trivial to state require some highly non-trivial analysis. We look at indefinite linear pencil problems from the perspective of a two parameter eigenvalue problem. We derive localisation results for real eigenvalues and present several examples. We also use different approaches to obtain estimates of non-real eigenvalues, supported by a large number of numerical experiments. Additionally, these experiments lead to various open questions and conjectures.
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