Applications of Bergman kernel functions

In this paper we revisit the so-called Bergman kernel method (BKM) for solving conformal mapping problems. This method is based on the reproducing property of the Bergman kernel function. The construction of reproducing kernel functions is not restricted to real dimension 2. Results concerning the construction of Bergman kernel functions in closed form for special domains in the framework of hypercomplex function theory suggest that BKM can also be extended to mapping problems in higher dimensions. We describe a 3-dimensional BKM-approach and present two numerical examples.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI)