New Eigenfunction Expansions and Alternative Representations for the Reduced Wave Equation

It has long been known that certain integral transforms and Fourier-type series can be used methodically for the resolution of certain kinds of classical boundary and initial value problems in separable coordinate systems. More recently, it has been shown that these classical transforms and series are spectral representations associated with an ordinary differential system which results on applying separation of variables to the given boundary value problem. This has been the basis for recent work concerned with systematically generating the proper spectral representation needed to solve a given problem. See [1] and [2] for a list of references.