Abstract and Applied Analysis (Jan 2013)

Explicit Spectral Decimation for a Class of Self-Similar Fractals

  • Sergio A. Hernández,
  • Federico Menéndez-Conde

DOI
https://doi.org/10.1155/2013/756075
Journal volume & issue
Vol. 2013

Abstract

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The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very symmetric. An explicit construction is given to obtain formulas for the eigenvalues of the Laplace operator acting on these fractals.