Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc
Volume 68 / 1998
Annales Polonici Mathematici 68 (1998), 227-236
DOI: 10.4064/ap-68-3-227-236
Abstract
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
