Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2565

 Title: Does Atkinson-Wilcox Expansion Converges for any Convex Domain? Authors: Arnaoudov, I.Georgiev, V.Venkov, G. Keywords: Atkinson-Wilcox Expansion TheoremHelmholtz EquationFar Field PatternConvex DomainSecond-Order Recurrence Relations Issue Date: 2007 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 33, No 2-3, (2007), 363p-376p Abstract: 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. Description: 2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40. URI: http://hdl.handle.net/10525/2565 ISSN: 1310-6600 Appears in Collections: Volume 33, Number 2-3

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