关于多重单代数域的指数变换
On the exponential transform of multi-sheeted algebraic domains
摘要：
我们引入多单版本的代数域和正交域，使他们能够分支覆盖面的黎曼球面。这两类域原来是相同的，和主要的结果表明，这种域的扩展指数变换同意，除了一些简单的因素，与扩展的消除功能的生成对的功能。在一个例子中，我们讨论的代数曲线相关联的水平曲线的诺依曼椭圆，并确定这些产生多片代数域。
英文摘要：
We introduce multi-sheeted versions of algebraic domains and quadrature domains, allowing them to be branched covering surfaces over the Riemann sphere. The two classes of domains turn out to be the same, and the main result states that the extended exponential transform of such a domain agrees, apart from some simple factors, with the extended elimination function for a generating pair of functions. In an example we discuss the algebraic curves associated to level curves of the Neumann oval, and determine which of these give rise to multi-sheeted algebraic domains.
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