Oberseminar Funktionentheorie, The dark side of the unit disk IV: Eigenspaces of the invariant Laplacian (Annika Moucha & Michael Heins)

We present a classification and a complete description of the Möbius-invariant eigenspaces of the generalized Laplacian on the complement of the complexified unit circle. The spectral theory of the invariant Laplacian on the unit disk, which has been developed by Helgason, Rudin and others, as well as the theory of the invariant Laplacian on the two--sphere are included as special cases. In principle, this talk is a continuation of the previous lectures, but we will carefully re-introduce all necessary tools, so that the talk will be essentially self-contained.