Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40. 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...