Karp’s theorem in electromagnetic scattering theory

Colton, David; Kress, Rainer

doi:10.1090/S0002-9939-1988-0964854-7

Karp’s theorem in electromagnetic scattering theory
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by David Colton and Rainer Kress PDF

Proc. Amer. Math. Soc. 104 (1988), 764-769 Request permission

Abstract:

Karp’s Theorem for acoustic waves states that if the far field pattern of the scattered wave corresponding to a plane wave incident upon an obstacle is only a function of the scalar product of the directions of incidence and observation then the obstacle is a ball. In this paper we shall give the analogue of Karp’s Theorem for the scattering of electromagnetic waves by a perfect conductor.

References

David Colton and Andreas Kirsch, Karp’s theorem in acoustic scattering theory, Proc. Amer. Math. Soc. 103 (1988), no. 3, 783–788. MR 947658, DOI 10.1090/S0002-9939-1988-0947658-0
David L. Colton and Rainer Kress, Integral equation methods in scattering theory, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 700400
David Colton and Rainer Kress, Dense sets and far field patterns in electromagnetic wave propagation, SIAM J. Math. Anal. 16 (1985), no. 5, 1049–1060. MR 800796, DOI 10.1137/0516078

Higher transcendental functions

Samuel N. Karp, Far field amplitudes and inverse diffraction theory, Electromagnetic waves, Univ. Wisconsin Press, Madison, Wis., 1962, pp. 291–300. MR 0129766
B. D. Sleeman, The inverse problem of acoustic scattering, IMA J. Appl. Math. 29 (1980), no. 2, 113–142. MR 679225, DOI 10.1093/imamat/29.2.113