On eigenvalue problems for the random walks on the Sierpinski pre-gaskets

  • Tadashi Shima


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.

Key words

eigenvalues Sierpinski pre-gasket decimation method 


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  1. [1]
    J. Kigami, A harmonic calculus on the Sierpinski spaces. Japan J. Appl. Math.,6 (1989), 259–290.zbMATHMathSciNetCrossRefGoogle Scholar
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    R. Rammal and G. Toulouse, Random walks on fractal structures and percolation clustars. J. Physique Lett.,43 (1982), L13-L22.Google Scholar
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    R. Rammal, Spectrum of harmonic excitations on fractals. J. Physique,45 (1984), 191–206.CrossRefMathSciNetGoogle Scholar

Copyright information

© JJIAM Publishing Committee 1991

Authors and Affiliations

  • Tadashi Shima
    • 1
  1. 1.Department of Mathematical Science, Faculty of Engineering ScienceOsaka UniversityOsakaJapan

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