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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 756075, 8 pages
http://dx.doi.org/10.1155/2013/756075
Research Article

Explicit Spectral Decimation for a Class of Self-Similar Fractals

Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, 42184 Pachuca, HGO, Mexico

Received 6 September 2012; Revised 22 December 2012; Accepted 3 January 2013

Academic Editor: Jiaxin Hu

Copyright © 2013 Sergio A. Hernández and Federico Menéndez-Conde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.