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
