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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/756075 |
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| _version_ | 1832552142741700608 |
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| author | Sergio A. Hernández Federico Menéndez-Conde |
| author_facet | Sergio A. Hernández Federico Menéndez-Conde |
| author_sort | Sergio A. Hernández |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-19ded2a7287a4ed3a5444abb3af76373 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-19ded2a7287a4ed3a5444abb3af763732025-02-03T05:59:28ZengWileyAbstract 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 |
| spellingShingle | Sergio A. Hernández Federico Menéndez-Conde Explicit Spectral Decimation for a Class of Self-Similar Fractals Abstract and Applied Analysis |
| title | 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_short | Explicit Spectral Decimation for a Class of Self-Similar Fractals |
| title_sort | explicit spectral decimation for a class of self similar fractals |
| url | http://dx.doi.org/10.1155/2013/756075 |
| work_keys_str_mv | AT sergioahernandez explicitspectraldecimationforaclassofselfsimilarfractals AT federicomenendezconde explicitspectraldecimationforaclassofselfsimilarfractals |