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Self-similar energies on post-critically finite self-similar fractals

Abstract:

On a large class of post-critically finite (finitely ramified) self-similar fractals with possibly little symmetry, we consider the question of existence and uniqueness of a Laplace operator. By considering positive refinement weights (local scaling factors) which are not necessarily equal, we show that for each such fractal, under a certain condition, there are corresponding refinement weights which support a unique self-similar Dirichlet form. As compared with previous results, our techniqu...

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Publication status:
Published

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Publisher copy:
10.1112/S002461070602312X

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Teplyaev, A More by this author
Journal:
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume:
74
Issue:
1
Pages:
93-112
Publication date:
2006-08-05
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
URN:
uuid:1db137ad-99df-48e1-963c-911ab75f9bde
Source identifiers:
5205
Local pid:
pubs:5205
Language:
English

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