Volume Doubling Measures and Heat Kernel Estimates on Self Similar Sets is popular PDF and ePub book, written by Jun Kigami in 2009-04-10, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Volume Doubling Measures and Heat Kernel Estimates on Self Similar Sets can be Read Online from any device for your convenience.
Volume Doubling Measures and Heat Kernel Estimates on Self Similar Sets Book PDF Summary
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.
Detail Book of Volume Doubling Measures and Heat Kernel Estimates on Self Similar Sets PDF
- Author : Jun Kigami
- Release : 10 April 2009
- Publisher : American Mathematical Soc.
- ISBN : 9780821842928
- Genre : Mathematics
- Total Page : 110 pages
- Language : English
- PDF File Size : 12,9 Mb
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