On the exponential transform of lemniscates
Complex Variables
2012-12-06 v1 Classical Analysis and ODEs
Operator Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1101.0794,
title = {On the exponential transform of lemniscates},
author = {Björn Gustafssom and Vladimir G. Tkachev},
journal= {arXiv preprint arXiv:1101.0794},
year = {2012}
}
Comments
19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verlag