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Title: Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
Authors: Arnaoudov, I.
Georgiev, V.
Venkov, G.
Keywords: Atkinson-Wilcox Expansion Theorem
Helmholtz Equation
Far Field Pattern
Convex Domain
Second-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.
ISSN: 1310-6600
Appears in Collections:Volume 33, Number 2-3

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