Explicit Spectral Decimation for a Class of Self-Similar Fractals

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 obtai...

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Main Authors:	Sergio A. Hernández, Federico Menéndez-Conde
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2013/756075

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spelling	doaj-19ded2a7287a4ed3a5444abb3af763732020-11-24T23:29:17ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/756075756075Explicit Spectral Decimation for a Class of Self-Similar FractalsSergio A. Hernández0Federico Menéndez-Conde1Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, 42184 Pachuca, HGO, MexicoCentro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, 42184 Pachuca, HGO, MexicoThe 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.http://dx.doi.org/10.1155/2013/756075
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Sergio A. Hernández Federico Menéndez-Conde
spellingShingle	Sergio A. Hernández Federico Menéndez-Conde Explicit Spectral Decimation for a Class of Self-Similar Fractals Abstract and Applied Analysis
author_facet	Sergio A. Hernández Federico Menéndez-Conde
author_sort	Sergio A. Hernández
title	Explicit Spectral Decimation for a Class of Self-Similar Fractals
title_short	Explicit Spectral Decimation for a Class of Self-Similar Fractals
title_full	Explicit Spectral Decimation for a Class of Self-Similar Fractals
title_fullStr	Explicit Spectral Decimation for a Class of Self-Similar Fractals
title_full_unstemmed	Explicit Spectral Decimation for a Class of Self-Similar Fractals
title_sort	explicit spectral decimation for a class of self-similar fractals
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2013-01-01
description	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.
url	http://dx.doi.org/10.1155/2013/756075
work_keys_str_mv	AT sergioahernandez explicitspectraldecimationforaclassofselfsimilarfractals AT federicomenendezconde explicitspectraldecimationforaclassofselfsimilarfractals
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Explicit Spectral Decimation for a Class of Self-Similar Fractals

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