Abstract
We describe recent results that establish a close relationship between the Ahlfors mapping function associated to an n-connected domain in the plane and the Bergman and Szegö kernels of the domain. The results show that the Ahlfors mapping plays a role in the multiply connected setting very similar to that of the Riemann mapping in the simply connected case. We also describe how the Ahlfors map is connected to the Poisson and other kernels.
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References
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© 1999 Springer Science+Business Media Dordrecht
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Bell, S.R. (1999). The Role of the Ahlfors Mapping in the Theory of Kernel Functions in the Plane. In: Saitoh, S., Alpay, D., Ball, J.A., Ohsawa, T. (eds) Reproducing Kernels and their Applications. International Society for Analysis, Applications and Computation, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2987-0_4
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DOI: https://doi.org/10.1007/978-1-4757-2987-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4809-0
Online ISBN: 978-1-4757-2987-0
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