Complex Analysis of Real Functions

III: Extended Fourier Theory

Jorge L. deLyra1

Department of Mathematical Physics, Physics Institute, University of São Paulo

August 24, 2017


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.