Event № 210
We study a compactification of certain graphs that goes back toideas of Royden. Given the boundary that arises from thiscompactification, we first study the Dirichlet problem. Secondly, inthe case of finite measure the associated Laplacians have purelydiscrete spectrum and one can give estimates on the eigenvalueasymptotics. Finally, the Markov extensions of the Laplacian can becharacterized by boundary conditions given by Dirichlet forms on theboundary.
(This comprises joint work with Agelos Georgakopoulos, SebastianHaeseler, Daniel Lenz, Marcel Schmidt, Michael Schwarz, RadoslawWojciechowski)