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Karp's theorem in electromagnetic scattering theory

Authors: David Colton and Rainer Kress
Journal: Proc. Amer. Math. Soc. 104 (1988), 764-769
MSC: Primary 78A45
MathSciNet review: 964854
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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.

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  • [1] D. Colton and A. Kirsch, Karp's theorem in acoustic scattering theory, Proc. Amer. Math. Soc. (to appear). MR 947658 (89h:35334)
  • [2] D. Colton and R. Kress, Integral equation methods in scattering theory, Wiley, New York, 1983. MR 700400 (85d:35001)
  • [3] -, Dense sets and far field patterns in electromagnetic wave propagation, SIAM J. Math. Anal. 16 (1985), 1049-1060. MR 800796 (86m:78009)
  • [4] A. Erdélyi, et. al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953.
  • [5] S. N. Karp, Far field amplitudes and inverse diffraction theory, Electromagnetic Waves (R. E. Langer, ed.), Univ. of Wisconsin Press, Madison, 1962, pp. 291-300. MR 0129766 (23:B2802)
  • [6] B. D. Sleeman, The inverse problem of acoustic scattering, IMA J. Appl. Math. 29 (1982), 113-142. MR 679225 (84c:76063)

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