Bergman's Integral Operator Method in Generalized Axially Symmetric Potential Theory
R. P. Gilbert
Source abstract
This paper contains a study of properties of solutions to the equation of generalized axially symmetric potentials. These potentials play an important role in many aspects of mathematical physics, in particular to an understanding of compressible flow in the transonic region. The ideas that have been basic in this investigation are contained in the integral operator method of Bergman. This method allows one to transplant certain properties of analytic functions to the solutions of linear partial differential equations. Results are obtained concerning singularities, residues, bounds, and growth of entire solutions, which are analogous to those found in classical function theory.
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