Mathematics – Complex Variables
Scientific paper
2011-01-04
Mathematics
Complex Variables
24 pages, to appear in CMFT journal (Computational Methods and Function Theory), a special volume "Constructive methods for co
Scientific paper
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.
Gustafsson Björn
Tkachev Vladimir G.
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