Analysis on Fractals: Index
Analysis on Fractals: Index
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DOI：
10.1017/cbo9780511470943
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发表时间：
2001-06
期刊：
影响因子：
3.1
通讯作者：
Jun Kigami
中科院分区：
文献类型：
--
作者：
Jun Kigami
本书涵盖了分形分析，这是数学的一个发展领域，重点关注分形的动力学方面，例如分形上的热扩散和具有分形结构的材料的振动。本书提供了对该主题的完整介绍，从自相似集的基本几何开始，继续讨论最近的结果，包括拉普拉斯算子的特征值和特征函数的性质，以及自相似集上热核的渐近行为。本书只需要高级分析、一般拓扑和测度论的基础知识，对于分析和概率论领域的研究生和研究人员来说很有价值。它也可用作分形研究生课程的补充教材。
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.