III: Extended Fourier Theory

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.

- Introduction

- Fourier Series
- Orthogonality Relations
- Completeness Relation
- Notes on the Convergence Problem
- Extension of the Theory
- Conclusions and Outlook
- Acknowledgments
- Appendix: Scalar Product for Inner Analytic Functions
- Bibliography