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On the exponential transform of multi-sheeted algebraic domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Computational methods in Function Theory, ISSN 1617-9447, Vol. 11, no 2, 591-615 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
algebraic domain, quadrature domain, exponential transform, elimination function, Riemann surface, Klein surface, Neumann’s oval
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-78806ISI: 000311620300010ScopusID: 2-s2.0-84871178114OAI: diva2:492909
Swedish Research Council

QC 20120412

Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2013-12-13Bibliographically approved

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