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 ; θ − α ) {F_0}(k;\theta - \alpha ) where k k is the wave number, θ \theta the angle of observation and α \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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