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Dirichlet forms on
the Sierpiński gasket
Robert Meyers, Robert S. Strichartz and Alexander Teplyaev |
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Vol. 217 (2004), No. 1, 149–174
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Abstract |
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We study not necessarily self-similar Dirichlet forms on the Sierpiński gasket that can be described as limits of compatible resistance networks on the sequence of graphs approximating the gasket. We describe the compatibility conditions in detail, and we also present an alternative description, based on just 3 conductance values and the 3-dimensional space of harmonic functions. In addition, we show how to parameterize all the Dirichlet forms by a set of independent variables. |
Milestones
Received: 15 September 2001
Published: 1 November 2004
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Authors |
| Robert Meyers | |
| New College University of South Florida Tampa FL 33620 |
Courant Institute NYU New York NY 10012 |
| Robert S. Strichartz | |
| Mathematics Department Cornell University Ithaca NY 14853 |
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| Alexander Teplyaev | |
| Mathematics Department University of Connecticut Storrs CT 06269 |
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