Atkinson-Wilcox Expansion Theorem Helmholtz Equation Far Field Pattern Convex Domain Second-Order Recurrence Relations
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 33, No 2-3, (2007), 363p-376p
The Atkinson-Wilcox theorem claims that any scattered field
in the exterior of a sphere can be expanded into a uniformly and absolutely
convergent series in inverse powers of the radial variable and that once
the leading coefficient of the expansion is known the full series can be
recovered uniquely through a recurrence relation. The leading coefficient of
the series is known as the scattering amplitude or the far field pattern of the
radiating field. In this work we give a simple characterization of the strictly
convex domains, such that a reasonable generalization of the AtkinsonWilcox expansion converges uniformly in the corresponding exterior domain.
All these strictly convex domains are spheres.