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- MORI Makoto
- Department of Mathematics College of Humanities and Sciences Nihon University
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- SUZUKI Osamu
- Department of Mathematics College of Humanities and Sciences Nihon University
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- WATATANI Yasuo
- Department of Mathematical Sciences Faculty of Mathematics Kyushu University
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抄録
We consider representations of Cuntz algebras on self-similar fractal sets for proper/improper systems of contractions. Natural representations, called Hausdorff representations, are associated with self-similar sets and Hausdorff measures in the case of similitudes in Rn. We completely classify the Hausdorff representations up to unitary equivalence. The complete invariant is the list(λ1D, . . . ,λND), where λj is the Lipschitz constant of the j th contraction and D is the Hausdorff dimension of the fractal set. Any non-trivial list can be realized by similitudes on the unit interval. There exists an improper system of contractions such that its representation of a Cuntz algebra on the self-similar fractal set is not unitarily equivalent to any Hausdorff representation for a proper system of similitudes in Rn.
収録刊行物
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- 九州数学雑誌
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九州数学雑誌 61 (2), 443-456, 2007
九州大学大学院数理学研究院
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詳細情報 詳細情報について
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- CRID
- 1390282680205477760
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- NII論文ID
- 110006377556
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- NII書誌ID
- AA10994346
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- ISSN
- 18832032
- 13406116
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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- 使用不可