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A version of Runge's theorem for the Helmholtz equation with applications to scattering theory*

Published online by Cambridge University Press:  20 January 2009

R. L. Ochs Jr
R. L. Ochs Jr
Affiliation:
Department of MathematicsThe University of ToledoToledoOhio 43606, USA
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Let D be a bounded, simply connected domain in the plane R2 that is starlike with respect to the origin and has C2, α boundary, ∂D, described by the equation in polar coordinates

where C2, α denotes the space of twice Hölder continuously differentiable functions of index α. In this paper, it is shown that any solution of the Helmholtz equation

in D can be approximated in the space by an entire Herglotz wave function

with kernel g ∈ L2[0,2π] having support in an interval [0, η] with η chosen arbitrarily in 0 > η < 2π.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 107 - 119
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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