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On the exponential transform of multi-sheeted algebraic domains
Mathematical department, KTH, 10044 Stockholm.
Mathematical department, KTH, 10044 Stockholm.ORCID iD: 0000-0002-8422-6140
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]
exponential transform; symmetric Riemann surface; algebraic functions
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-79618OAI: diva2:577357
Available from: 2012-12-15 Created: 2012-08-11 Last updated: 2014-10-08

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Tkachev, Vladimir
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Computational methods in Function Theory
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