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Decomposition theorems for the generalized metaharmonic equation in several independent variables

Published online by Cambridge University Press:  09 April 2009

David Colton
David Colton
Affiliation:
Department of Mathematics McGill UniversityMontreal, Canada
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In this paper solutions of the generalized metaharmonic equation in several independent variables where λ > 0 are uniquely decomposed into the sum of a solution regular in the entire space and one satisfying a generalized Sommerfeld radiation condition. Due to the singular nature of the partial differential equation under investigation it is shown that the radiation condition in general must hold uniformly in a domain lying in the space of several complex variables. This result indicates that function theoretic methods are not only the correct and natural avenue of approach in the study of singular ordinary differential equations, but are basic in the investigation of singular partial differential equations as well.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 35 - 46
Copyright
Copyright © Australian Mathematical Society 1972

References

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