Generalizing the Classical Theory: A Naive Approach
Many functions encountered in everyday applications — including all nonzero constant functions periodic functions, exponentials and polynomials — are not classically transformable. As a result, the purely classical theory for Fourier transforms is too limited for many applications. Fortunately, there is a more general theory under which many more functions, including all of those mentioned above, are “Fourier transformable”. This theory, which we will refer to as the “generalized theory” since it generalizes the classical theory, will be developed, as rigorously and completely as we can, in part IV of this text.
Admittedly, however, a reasonably rigorous and complete development of the ...
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