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 A. Erdélyi, et. al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953.
- Samuel N. Karp, Far field amplitudes and inverse diffraction theory, Electromagnetic waves, Univ. Wisconsin Press, Madison, Wis., 1962, pp. 291–300. MR 0129766
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 764-769
- MSC: Primary 78A45
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964854-7
- MathSciNet review: 964854