**Further spectral properties of uniformly elliptic operators that include a non-local term.** / Dodds, Niall.

Research output: Contribution to journal › Article

Dodds, N 2008, 'Further spectral properties of uniformly elliptic operators that include a non-local term' *Applied Mathematics and Computation*, vol 197, no. 1, pp. 317-327., 10.1016/j.amc.2007.07.049

Dodds, N. (2008). Further spectral properties of uniformly elliptic operators that include a non-local term. *Applied Mathematics and Computation*, *197*(1), 317-327. 10.1016/j.amc.2007.07.049

Dodds N. Further spectral properties of uniformly elliptic operators that include a non-local term. Applied Mathematics and Computation. 2008 Mar;197(1):317-327. Available from: 10.1016/j.amc.2007.07.049

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title = "Further spectral properties of uniformly elliptic operators that include a non-local term",

keywords = "Non-local differential operators, Uniformly elliptic operators, Eigenvalues, Integro-differential operators",

author = "Niall Dodds",

note = "dc.publisher: Elsevier",

year = "2008",

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N2 - 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.

AB - 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.

KW - Non-local differential operators

KW - Uniformly elliptic operators

KW - Eigenvalues

KW - Integro-differential operators

U2 - 10.1016/j.amc.2007.07.049

DO - 10.1016/j.amc.2007.07.049

M3 - Article

VL - 197

SP - 317

EP - 327

JO - Applied Mathematics and Computation

T2 - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

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