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Asymptotic Eigenfunctions of a Scattering Problem
S. E. Shamma and S. N. Karp
SIAM Journal on Applied Mathematics
Vol. 22, No. 1 (Jan., 1972), pp. 14-21
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2100128
Page Count: 8
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Previously we discussed a generalization of separability in boundary value problems arising in potential theory. In this paper we extend the results to the scattering problems. The method is based on an integral equation whose kernel is the two-dimensional free space Green's function (i/4)H(1) 0(k|r - r'|), where |r - r'| is the distance between two points on the scatterer. The asymptotic behavior of the eigenvalues and eigenfunctions of a larger class of kernels is obtained. This class includes the second iterated kernel of the above Green's function. It includes also the kernel N0(k|r - r'|) which arises in the study of several physical situations. The results are confirmed in a special case.
SIAM Journal on Applied Mathematics © 1972 Society for Industrial and Applied Mathematics