发表机构
Afeka Academic College of Engineering（阿菲卡工程学术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出以柯西型卷积积分在同伦类上的良定义为核心问题，发展复分析基础结果，并区分实分析与复分析共享规则的工具箱，展示其解释价值及与既有表述的关系。
AI 中文摘要
在三种既有的初等复分析表述之外，我们提出了一种以单一组织性问题为中心的方法：轮廓卷积在何时于同伦类上有良好定义？从这一起点出发，我们发展了该学科的基础结果。一个支持性的概念区分识别出实分析与复分析中共享相同运算和符号规则的元素。我们将这一集合称为“工具箱”。示例和结构联系展示了该方法在理论不同方面的解释价值与覆盖范围。我们还考察了我们的方法与既有表述之间的关系。
英文摘要
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.
Comments27 pages
