Potential Theory

doi:10.1007/978-1-4613-0981-9

1988

DOI: 10.1007/978-1-4613-0981-9

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Potential Theory

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2012

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On the Exponential Transform of Multi-Sheeted Algebraic Domains

Gustafsson

Tkachev

2012

Comput. Methods Funct. Theory

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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.

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On the Exponential Transform of Multi-Sheeted Algebraic Domains

Gustafsson

Tkachev

2012

Comput. Methods Funct. Theory

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Potential Theory

Cited by 1 publication

References 16 publications

On the Exponential Transform of Multi-Sheeted Algebraic Domains

On the Exponential Transform of Multi-Sheeted Algebraic Domains

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