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

Presented by: 
A Teplyaev [Connecticut]
Tuesday 15th May 2007 -
14:30 to 15:30
INI Seminar Room 1

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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons