Atkinson—wilcox Expansion Theorem for Inhomogeneous Media

The classical Atkinson-Wilcox theorem claims that in the exterior of the sphere that optimally circumscribes the scatterer, any radiating solution to the Helmholtz equation can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial distance. Moreover, the full series can be recovered uniquely through a second-order recurrence relation via the leading coefficient, known as the far-field pattern. In this work we consider the medium scattering problem and prove an analogue of the expansion theorem for inhomogeneity of compact support.