  In the context of the complex-analytic structure within the unit disk
centered at the origin of the complex plane, that was presented in a previous
paper, we show that the complete Fourier theory of integrable real functions is
contained within that structure, that is, within the structure of the space of
inner analytic functions on the open unit disk. We then extend the Fourier
theory beyond the realm of integrable real functions, to include for example
singular Schwartz distributions, and possibly other objects.
