3 papers
math.CV2004
The Bergman kernel and quadrature domains in the plane
Steven R. Bell
A streamlined proof that the Bergman kernel associated to a quadrature domain in the plane must be algebraic will be given. A byproduct of the proof will be that the Bergman kernel…
math.CV2002
Mobius transformations, the Caratheodory metric, and the objects of complex analysis and potential theory in multiply connected domains
Steven R. Bell
It is proved that the family of Ahlfors extremal mappings of a multiply connected region in the plane onto the unit disc can be expressed as a rational combination of two fixed Ahl…
math.CV1998
Finitely generated function fields and complexity in potential theory in the plane
Steven R. Bell
We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex var…