On the exponential transform of lemniscates

Details On the exponential transform of lemniscates On the exponential transform of lemniscates

2011-01-04

arxiv.org/abs/1101.0794v1

Mathematics

Complex Variables

19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in M

Scientific paper

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.

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