TY  - JOUR
T1  - Further spectral properties of uniformly elliptic operators that include a non-local term
A1  - Dodds,Niall
AU  - Dodds,Niall
PY  - 2008/3
Y1  - 2008/3
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
M1  - Article
JO  - Applied Mathematics and Computation
JF  - Applied Mathematics and Computation
SN  - 0096-3003
IS  - 1
VL  - 197
SP  - 317
EP  - 327
ER  -