# Szegö limit theorems on the Sierpinski gasket

by Kasso A. Okoudjou, Luke G. Rogers, Robert S. Strichartz

We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket to formulate and prove analogues of the strong Szego limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences. Continue reading

# Laplacians on the basilica Julia set

by Luke G Rogers and Alexander Teplyaev.

We consider the basilica Julia set of the polynomial $$P(z)=z^{2}-1$$ and construct all possible
resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topology in the
effective resistance metric coincides with the usual topology. Continue reading