The Schottky–Klein prime function: a theoretical and computational tool for applications
The Schottky–Klein prime function: a theoretical and computational tool for applications
复制标题
肖特基-克莱因素数函数：应用的理论和计算工具
DOI：
10.1093/imamat/hxw028
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发表时间：
2016
影响因子：
1.2
通讯作者：
Mohamed M. S. Nasser
中科院分区：
文献类型：
--
作者：
D. Crowdy;E. Kropf;Christopher C. Green;Mohamed M. S. Nasser
本文综述了所谓的肖特基-克莱因素函数在各种应用数学背景下所起的重要作用。虽然它是一个经典的特殊函数，由19世纪的研究者提出，但它的理论意义在最近十几年才被认识到，特别是在解决多连通区域中的DefifiNed问题方面。在这方面，许多仅与单连通(无洞)有关的众所周知的结果可以自然地推广到多重连通的情形，从而使这些众所周知的结果在更一般的框架内具有更广泛的适用性。鉴于肖特基-克莱因素函数的广泛用途，能够科学地计算它是很重要的。在这里，我们介绍了一种新的计算理论公式，以及实现该构造的两种不同的数值方法。这些理论和计算发展的结合使得肖特基-克莱因素函数成为应用数学中一个强大的新工具。
This paper surveys the important role, in a variety of applied mathematical contexts, played by the so-called Schottky-Klein prime function. While it is a classical special function, introduced by 19th century investigators, its theoretical significance for applications has only been realized in the last decade or so, especially with respect to solving problems defined in multiply connected, or “holey”, domains. It is shown here that, in terms of it, many well-known results pertaining only to the simply connected case (no holes) can be generalized, in a natural way, to the multiply connected case thereby contextualizing those well-known results within a more general framework of much broader applicability. Given the wide-ranging usefulness of the Schottky-Klein prime function it is important to be able to compute it efficiently. Here we introduce both a new theoretical formulation for its computation, as well as two distinct numerical methods to implement the construction. The combination of these theoretical and computational developments renders the Schottky-Klein prime function a powerful new tool in applied mathematics.
影响因子：
3.4
作者：
Crowdy D
通讯作者：
Crowdy D
肖特基双平面域上的肖特基-克莱因素函数
影响因子：
2.1
作者：
Crowdy D
通讯作者：
Crowdy D
计算肖特基双平面域上的肖特基-克莱因素数函数
影响因子：
2.1
作者：
Crowdy D
通讯作者：
Crowdy D