| eBook ISBN: | 978-1-4704-0538-0 |
| Product Code: | MEMO/199/932.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
| eBook ISBN: | 978-1-4704-0538-0 |
| Product Code: | MEMO/199/932.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 199; 2009; 94 ppMSC: Primary 28; 60; Secondary 31
This paper studies the following three problems.
1. When does a measure on a self-similar set have the volume doubling property with respect to a given distance?
2. Is there any distance on a self-similar set under which the contraction mappings have the prescribed values of contractions ratios?
3. When does a heat kernel on a self-similar set associated with a self-similar Dirichlet form satisfy the Li-Yau type sub-Gaussian diagonal estimate?
These three problems turn out to be closely related. The author introduces a new class of self-similar set, called rationally ramified self-similar sets containing both the Sierpinski gasket and the (higher dimensional) Sierpinski carpet and gives complete solutions of the above three problems for this class. In particular, the volume doubling property is shown to be equivalent to the upper Li-Yau type sub-Gaussian diagonal estimate of a heat kernel.
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Table of Contents
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Chapters
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Prologue
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Chapter 1. Scales and volume doubling property of measures
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Chapter 2. Construction of distances
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Chapter 3. Heat kernel and volume doubling property of measures
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Appendix
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This paper studies the following three problems.
1. When does a measure on a self-similar set have the volume doubling property with respect to a given distance?
2. Is there any distance on a self-similar set under which the contraction mappings have the prescribed values of contractions ratios?
3. When does a heat kernel on a self-similar set associated with a self-similar Dirichlet form satisfy the Li-Yau type sub-Gaussian diagonal estimate?
These three problems turn out to be closely related. The author introduces a new class of self-similar set, called rationally ramified self-similar sets containing both the Sierpinski gasket and the (higher dimensional) Sierpinski carpet and gives complete solutions of the above three problems for this class. In particular, the volume doubling property is shown to be equivalent to the upper Li-Yau type sub-Gaussian diagonal estimate of a heat kernel.
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Chapters
-
Prologue
-
Chapter 1. Scales and volume doubling property of measures
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Chapter 2. Construction of distances
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Chapter 3. Heat kernel and volume doubling property of measures
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Appendix
