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Spectra of indefinite linear operator pencils

Ozturk, H. M. (2019) Spectra of indefinite linear operator pencils. PhD thesis, University of Reading

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Abstract/Summary

In 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.

Item Type:Thesis (PhD)
Thesis Supervisor:Levitin, M.
Thesis/Report Department:School of Mathematical, Physical and Computational Sciences
Identification Number/DOI:
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:85871

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