The Compositional Integral: The Narrow And The Complex Looking-Glass
General Mathematics
2020-11-03 v4
Abstract
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at recovering Cauchy's Integral Formula. With this we derive a modified form of Cauchy's Residue Theorem. Then, we develop a compositional analogue of Taylor Series. In finality, we describe a compositional Fourier Transform; and illustrate some basic properties of it.
Cite
@article{arxiv.2003.05280,
title = {The Compositional Integral: The Narrow And The Complex Looking-Glass},
author = {James David Nixon},
journal= {arXiv preprint arXiv:2003.05280},
year = {2020}
}