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.

**[1]**David Colton and Andreas Kirsch,*Karp’s theorem in acoustic scattering theory*, Proc. Amer. Math. Soc.**103**(1988), no. 3, 783–788. MR**947658**, 10.1090/S0002-9939-1988-0947658-0**[2]**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****[3]**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**, 10.1137/0516078**[4]**A. Erdélyi, et. al.,*Higher transcendental functions*, Vol. II, McGraw-Hill, New York, 1953.**[5]**Samuel N. Karp,*Far field amplitudes and inverse diffraction theory*, Electromagnetic waves, Univ. of Wisconsin Press, Madison, Wis., 1962, pp. 291–300. MR**0129766****[6]**B. D. Sleeman,*The inverse problem of acoustic scattering*, IMA J. Appl. Math.**29**(1980), no. 2, 113–142. MR**679225**, 10.1093/imamat/29.2.113

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0964854-7

Article copyright:
© Copyright 1988
American Mathematical Society