JournalsjfgVol. 6 , No. 2pp. 143–156

Non-degeneracy of the harmonic structure on Sierpiński gaskets

  • Konstantinos Tsougkas

    Uppsala University, Sweden
Non-degeneracy of the harmonic structure on Sierpiński gaskets cover
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Abstract

We prove that the harmonic extension matrices for the two dimensional level-kk Sierpiński gasket are invertible for every k2k \geq 2. This has been previously conjectured to be true by Hino in [10] and [11] and tested numerically for k50k \leq 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.

Cite this article

Konstantinos Tsougkas, Non-degeneracy of the harmonic structure on Sierpiński gaskets. J. Fractal Geom. 6 (2019), no. 2 pp. 143–156

DOI 10.4171/JFG/73