分形上的小波
经典分析与常微分方程
2007-05-23 v4 泛函分析
摘要
我们在分数维介于0与1之间的Hausdorff测度背景下发展了多分辨率理论。尽管我们的分形小波理论与线上Lebesgue测度的标准情形有若干相似之处，但也存在鲜明对比。这些对比表述于我们的主要结果——一个二分定理中。第一节是三分之一中部Cantor集的情形。随后回顾了关于Hausdorff测度的要点。论文其余部分涵盖了仿射迭代函数系统一般背景下的多分辨率。
引用
@article{arxiv.math/0305443,
title = {Wavelets on Fractals},
author = {Dorin E. Dutkay and Palle E. T. Jorgensen},
journal= {arXiv preprint arXiv:math/0305443},
year = {2007}
}
备注
We have followed all the suggestions and corrections made by the referee. In the introduction, we added an overview of the three themes in the paper, and added some motivation. This was motivated by the comments and suggestions of the referee. We also rearranged the material as suggested by the referee. This makes the three themes in our paper more clear, we believe