Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

Arnaoudov, I., Georgiev, V., and Venkov, G.. "Does Atkinson-Wilcox Expansion Converges for any Convex Domain?." Serdica Mathematical Journal 33.2-3 (2007): 363-376. <http://eudml.org/doc/281407>.

@article{Arnaoudov2007,
abstract = {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 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.},
author = {Arnaoudov, I., Georgiev, V., Venkov, G.},
journal = {Serdica Mathematical Journal},
keywords = {Atkinson-Wilcox Expansion Theorem; Helmholtz Equation; Far Field Pattern; Convex Domain; Second-Order Recurrence Relations; Atkinson-Wilcox expansion theorem; Helmholtz equation; far field pattern; convex domain; second-order recurrence relations},
language = {eng},
number = {2-3},
pages = {363-376},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Does Atkinson-Wilcox Expansion Converges for any Convex Domain?},
url = {http://eudml.org/doc/281407},
volume = {33},
year = {2007},
}

TY - JOUR
AU - Arnaoudov, I.
AU - Georgiev, V.
AU - Venkov, G.
TI - Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
JO - Serdica Mathematical Journal
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 33
IS - 2-3
SP - 363
EP - 376
AB - 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 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.
LA - eng
KW - Atkinson-Wilcox Expansion Theorem; Helmholtz Equation; Far Field Pattern; Convex Domain; Second-Order Recurrence Relations; Atkinson-Wilcox expansion theorem; Helmholtz equation; far field pattern; convex domain; second-order recurrence relations
UR - http://eudml.org/doc/281407
ER -