Non-degeneracy of the harmonic structure on Sierpinski Gaskets

2016/05/13 by Tsougkas, Konstantinos · 1 citation
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1605.04117

Abstract

We prove that the harmonic extension matrices for the level-k Sierpinski Gasket are invertible for every k>2. This has been previously conjectured to be true by Hino in [6] and [7] and tested numerically for k<50. We also give a necessary condition for the non-degeneracy of the harmonic structure for general finitely ramified self-similar sets based on the vertex connectivity of their first graph approximation.

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• L^p-Integrability of Radon-Nikodym Densities Between Harmonic Energy Measures on the Sierpinski Gasket

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