Mathematical Sciences: Conference: "Wavelets and Fractals"

9319086 Lau该奖项为将于1994年5月20-22日在匹兹堡大学举行的小波和分形会议提供部分支持。会议将介绍小波和分形的各个方面和联系的研究；函数与分形测度的小波分解、重构与采样双尺度膨胀方程的存在性及规律性谐波分析中的自相似；测度的多重分形结构、多维小波和自相似拼接。小波是近年来谐波分析数学领域的新发展。它结合了传统的希尔伯特空间方法和单个函数（小波）的膨胀和平移基的新构造。除了在计算上的优势外，人们还发现小波在时间和频率上都是局部的，这使得它们在信号处理中的应用特别有效。＊＊＊

9319086 Lau This award provides partial support for a conference on wavelets and fractals to be held at the University of Pittsburgh, May 20-22, 1994. The conference will present studies on various aspects and connections of wavelets and fractals; wavelet decomposition, reconstruction and sampling of functions and fractal measures; existence and regularity of the two-scale dilation equations; self-similarity in harmonic analysis; multifractal structure of measures and multi-dimensional wavelets and self-similar tilings. Wavelets is a recently new development in the mathematical area of harmonic analysis. It combines traditional Hilbert space methods with new constructions of bases from dilations and translations of a single function (the wavelet). In addition to computational advantages in this approach, it has been found that wavelets can be found which are local in both time and frequency making their application to signal processing particularly effective. ***