Geodesic
Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
Serdica Mathematical Journal, Tome 33 (2007) no. 2-3, pp. 363-376

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Atkinson-Wilcox Expansion Theorem, Helmholtz Equation, Far Field Pattern, Convex Domain, Second-Order Recurrence Relations 
@article{SMJ2_2007_33_2-3_a8,
     author = {Arnaoudov, I. and Georgiev, V. and Venkov, G.},
     title = {Does {Atkinson-Wilcox} {Expansion} {Converges} for any {Convex} {Domain?}},
     journal = {Serdica Mathematical Journal},
     pages = {363--376},
     publisher = {mathdoc},
     volume = {33},
     number = {2-3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2007_33_2-3_a8/}
}
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
SP  - 363
EP  - 376
VL  - 33
IS  - 2-3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2007_33_2-3_a8/
LA  - en
ID  - SMJ2_2007_33_2-3_a8
ER  - 
%0 Journal Article
%A Arnaoudov, I.
%A Georgiev, V.
%A Venkov, G.
%T Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
%J Serdica Mathematical Journal
%D 2007
%P 363-376
%V 33
%N 2-3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2007_33_2-3_a8/
%G en
%F SMJ2_2007_33_2-3_a8
Arnaoudov, I.; Georgiev, V.; Venkov, G. Does Atkinson-Wilcox Expansion Converges for any Convex Domain?. Serdica Mathematical Journal, Tome 33 (2007) no. 2-3, pp. 363-376. http://geodesic.mathdoc.fr/item/SMJ2_2007_33_2-3_a8/