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arXiv · 2003.05280

The Compositional Integral: The Narrow And The Complex Looking-Glass

James David Nixon
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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.

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James David Nixon. 2020-03-06. The Compositional Integral: The Narrow And The Complex Looking-Glass. https://arxiv.org/abs/2003.05280

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