Complex Analysis of Real Functions
III: Extended Fourier Theory
Jorge L. deLyra1
Department of Mathematical Physics,
Physics Institute,
University of São Paulo
May 26, 2018
Abstract:
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.