Uniqueness theorems for a class of singular partial differential equations
Colton, David L.
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Of fundamental importance in physics are problems whose mathematical formulation requires at least three dimensions. Since in many ways one and two dimensional problems are easier to handle, one of the major efforts of mathematicians has been to reduce three dimensional problems to those of lower dimensions. Fourier analysis, separation of variables, integral transforms, and the introduction of various kinds of axial symmetry are some of the more familiar methods that have been devised with this aim in mind. This thesis is concerned with the study of the two dimensional equations that result when Fourier analysis is applied to the three dimensional Helmholtz or reduced wave equation.