Abstract
We work with increasing finite setsV m called pre-gaskets approximating the finite Sierpinski gasket located inR N−1 (N ≥ 3). The eigenvalues of the discrete Laplacian onV m under the Dirichlet and Neumann boundary conditions are completely determined using the decimation method due to Rammal.
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References
J. Kigami, A harmonic calculus on the Sierpinski spaces. Japan J. Appl. Math.,6 (1989), 259–290.
R. Rammal and G. Toulouse, Random walks on fractal structures and percolation clustars. J. Physique Lett.,43 (1982), L13-L22.
R. Rammal, Spectrum of harmonic excitations on fractals. J. Physique,45 (1984), 191–206.
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The author would like to thank Professor M. Fukushima and the referee for the most helpful suggestions.
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Shima, T. On eigenvalue problems for the random walks on the Sierpinski pre-gaskets. Japan J. Indust. Appl. Math. 8, 127–141 (1991). https://doi.org/10.1007/BF03167188
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DOI: https://doi.org/10.1007/BF03167188