45 citations · 146 across the 29 of their papers we have counts for
3 papers · 1 filter
The resolvent kernel for PCF self-similar fractals
Marius Ionescu, Erin P. J. Pearse, Luke G. Rogers +2
For the Laplacian defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also w…
Szego limit theorems on the Sierpinski gasket
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 settin…
Laplacians on the basilica Julia set
Luke G. Rogers, Alexander Teplyaev
We consider the basilica Julia set of the polynomial and construct all possible resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topolog…