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Cauchy-Type Convolution Integrals as the Starting Point for a First Encounter with Complex Analysis
Abstract
Alongside three established presentations of elementary complex analysis, we propose an approach centered on one organizing question: when is contour convolution well defined on homotopy classes? From this starting point, we develop the foundational results of the subject. A supporting conceptual distinction identifies those elements of real and complex analysis that share the same operational and symbolic rules. We refer to this collection as the "Toolbox." Examples and structural connections illustrate the explanatory value and reach of the approach across different aspects of the theory. We also examine the relationship of our approach to the established presentations.
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BibTeX
@misc{bensimon2026cauchytype,
title = {{Cauchy-Type Convolution Integrals as the Starting Point for a First Encounter with Complex Analysis}},
author = {Gabriel Ben-Simon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05612},
eprint = {2610.05612},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05612},
}
RIS
TY - UNPB
TI - Cauchy-Type Convolution Integrals as the Starting Point for a First Encounter with Complex Analysis
AU - Gabriel Ben-Simon
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05612
UR - https://arxiv.org/abs/2610.05612
AB - Alongside three established presentations of elementary complex analysis, we propose an approach centered on one organizing question: when is contour convolution well defined on homotopy classes? From this starting point, we develop the foundational results of the subject. A supporting conceptual distinction identifies those elements of real and complex analysis that share the same operational and symbolic rules. We refer to this collection as the "Toolbox." Examples and structural connections illustrate the explanatory value and reach of the approach across different aspects of the theory. We also examine the relationship of our approach to the established presentations.
ER -