# Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

Arnaoudov, I.; Georgiev, V.; Venkov, G.

Serdica Mathematical Journal (2007)

- Volume: 33, Issue: 2-3, page 363-376
- ISSN: 1310-6600

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topArnaoudov, 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 -

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