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Integral operator methods for generalized axially symmetric potentials in (n+1) variables*

Published online by Cambridge University Press:  09 April 2009

R. P. Gilbert  and
H. C. Howard
R. P. Gilbert
Affiliation:
Georgetown University, Washington, D.C.
H. C. Howard
Affiliation:
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin.
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In this paper we shall use the integral operator method of Bergman, B[1–6], to investigate solutions of the partial differential equation where s > −1. In particular, information concerning the growth, and location of singularities, of solutions of (1.1) will be obtained. Equations of the form (1.1) with s = 1, 2, arise from the (n+k+1)-dimensional Laplace equation Δn+k+1u = 0 in the “axially symmetric” coordinates x1, …xn, p where the relationship between cartesian and “axially symmetric” coordinates is given by

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 3 , August 1965 , pp. 331 - 348
Copyright
Copyright © Australian Mathematical Society 1965

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