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

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    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.
    Original languageEnglish
    Pages (from-to)317-327
    Number of pages11
    JournalApplied Mathematics and Computation
    Volume197
    Issue number1
    DOIs
    Publication statusPublished - Mar 2008

    Keywords

    • Non-local differential operators
    • Uniformly elliptic operators
    • Eigenvalues
    • Integro-differential operators

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