On the exponential transform of multi-sheeted algebraic domains
2011 (English)In: Computational methods in Function Theory, ISSN 1617-9447, Vol. 11, no 2, 591-615 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2011. Vol. 11, no 2, 591-615 p.
algebraic domain, quadrature domain, exponential transform, elimination function, Riemann surface, Klein surface, Neumann’s oval
IdentifiersURN: urn:nbn:se:kth:diva-78806ISI: 000311620300010ScopusID: 2-s2.0-84871178114OAI: oai:DiVA.org:kth-78806DiVA: diva2:492909
FunderSwedish Research Council
QC 201204122012-02-082012-02-082013-12-13Bibliographically approved