Isaac Newton Institute for Mathematical Sciences

Schur complement, Drichlet-to-Neumann map, and eigenfunctions on self-similar graphs

15th May 2007

Author: Alexander Teplyaev (Connecticut)

Abstract

We study eigenvalues and eigenfunctions on the class of self-similar symmetric finitely ramified graphs. We consider such examples as the graphs modeled on the Sierpinski gasket, a non-p.c.f. analog of the Sierpinski gasket, the Level-3 Sierpinski gasket, a fractal 3-tree, the Hexagasket, and one dimensional fractal graphs. We develop a matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly.