On the exponential transform of multi-sheeted algebraic domains
Complex Variables
2018-04-20 v1
Abstract
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.
Cite
@article{arxiv.1101.0799,
title = {On the exponential transform of multi-sheeted algebraic domains},
author = {Björn Gustafsson and Vladimir G. Tkachev},
journal= {arXiv preprint arXiv:1101.0799},
year = {2018}
}
Comments
24 pages, to appear in CMFT journal (Computational Methods and Function Theory), a special volume "Constructive methods for compact Riemann surfaces in applications"