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

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

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

Article copyright:
© Copyright 1988
American Mathematical Society