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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Karp’s theorem in acoustic scattering theory
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by David Colton and Andreas Kirsch
Proc. Amer. Math. Soc. 103 (1988), 783-788
DOI: https://doi.org/10.1090/S0002-9939-1988-0947658-0

Abstract:

Karp’s Theorem states that if the far field pattern corresponding to the scattering of a time harmonic plane acoustic wave by a sound-soft cylinder is of the form ${F_0}(k;\theta - \alpha )$ where $k$ is the wave number, $\theta$ the angle of observation and $\alpha$ the angle of incidence of the plane wave, then the cylinder must be circular. A new proof is given of this result and extended to the cases of scattering by a sound-hard obstacle and an inhomogeneous medium.
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 783-788
  • MSC: Primary 35R30; Secondary 35J05, 35P25, 76Q05
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947658-0
  • MathSciNet review: 947658