I: Complex-Analytic Structure and

Integrable Real Functions

A complex-analytic structure within the unit disk of the complex plane
is presented. It can be used to represent and analyze a large class of
real functions. It is shown that any integrable real function can be
obtained by means of the restriction of an analytic function to the unit
circle, including functions which are non-differentiable, discontinuous
or unbounded. An explicit construction of the analytic functions from
the corresponding real functions is given. The complex-analytic
structure can be understood as an universal regulator for analytic
operations on real functions.

- Introduction
- Definitions and Properties
- Representation of Integrable Real Functions
- Behavior Under Analytic Operations
- Conclusions and Outlook
- Acknowledgments
- Bibliography