Self-similar energies on post-critically finite self-similar fractals
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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2006
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| _version_ | 1826262145211301888 |
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| author | Hambly, B Metz, V Teplyaev, A |
| author_facet | Hambly, B Metz, V Teplyaev, A |
| author_sort | Hambly, B |
| collection | OXFORD |
| description | 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 technique allows us to replace symmetry by connectivity arguments. © 2006 London Mathematical Society. |
| first_indexed | 2024-03-06T19:31:45Z |
| format | Journal article |
| id | oxford-uuid:1db137ad-99df-48e1-963c-911ab75f9bde |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:31:45Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:1db137ad-99df-48e1-963c-911ab75f9bde2022-03-26T11:12:19ZSelf-similar energies on post-critically finite self-similar fractalsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1db137ad-99df-48e1-963c-911ab75f9bdeEnglishSymplectic Elements at Oxford2006Hambly, BMetz, VTeplyaev, AOn 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 technique allows us to replace symmetry by connectivity arguments. © 2006 London Mathematical Society. |
| spellingShingle | Hambly, B Metz, V Teplyaev, A Self-similar energies on post-critically finite self-similar fractals |
| title | Self-similar energies on post-critically finite self-similar fractals |
| title_full | Self-similar energies on post-critically finite self-similar fractals |
| title_fullStr | Self-similar energies on post-critically finite self-similar fractals |
| title_full_unstemmed | Self-similar energies on post-critically finite self-similar fractals |
| title_short | Self-similar energies on post-critically finite self-similar fractals |
| title_sort | self similar energies on post critically finite self similar fractals |
| work_keys_str_mv | AT hamblyb selfsimilarenergiesonpostcriticallyfiniteselfsimilarfractals AT metzv selfsimilarenergiesonpostcriticallyfiniteselfsimilarfractals AT teplyaeva selfsimilarenergiesonpostcriticallyfiniteselfsimilarfractals |