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Further spectral properties of uniformly elliptic operators that include a non-local term

Further spectral properties of uniformly elliptic operators that include a non-local term

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Authors

  • Niall Dodds

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Info

Original languageEnglish
Pages317-327
Number of pages11
JournalApplied Mathematics and Computation
Journal publication dateMar 2008
Journal number1
Volume197
DOIs
StatePublished

Abstract

In this paper we consider the eigenvalues of a class of non-local differential operators. The real eigenvalues of certain examples of these operators have previously been plotted (as functions of a fundamental parameter in the operator), using appropriate computer software. Here we show how the complex eigenvalues of such operators may also be plotted. We use the plots of both the real and the complex eigenvalues to motivate a number of new theoretical results regarding the structure of the spectrum, which we subsequently prove under suitable hypotheses.

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