ABSTRACT
Some problems of practical importance are beyond the reach of the method of eigenfunction expansion. This is the case, for example, when the space variable is defined on the entire real line and where, as a consequence, there are no boundary points. This may lead to the problem in question having a continuum of eigenvalues instead of a countable set. In such situations we need to employ other techniques of solution. The Fourier transformationsdeveloped, in fact, from the Fourier series representations of functions-are particularly useful tools when dealing with infinite or semi-infinite spatial regions because they are designed for exactly this type of setup and have the added advantage that they reduce by one the number of “active” variables in the given PDE problem.
