A conference on interaction between wavelets and splines

提议的研讨会将提供一个论坛，促进小波和样条领域研究人员的互动。样条函数的研究是一个成熟的研究课题，在过去的三四十年中已经成为一个跨学科的研究领域，而小波的研究仅在二十年前才诞生。然而，唯一已知的紧支持函数与解析公式，产生一个多分辨率近似是基数b样条。此外，b样条细化符号在Daubechies小波的构造中发挥核心作用，通过确保构成Daubechies尺度函数的傅里叶变换的某些无限乘积的收敛性以及这些函数的平滑顺序，作为MRA的构建块。样条曲线和小波之间的密切关系是这两个跨学科数学研究领域相互作用的根本需求。这次关于小波和样条之间相互作用的会议将汇集这两个领域的顶尖专家交流思想，评估最新技术，并确定未来研究问题的趋势，这两个跨学科领域都将受益。更重要的是，这样的会议将大大有利于年轻的研究人员和弱势群体，他们将有非常有限的机会，如果有的话，在同一屋檐下与这两个学科的主要专家进行互动。这次会议将于2005年16-19日在乔治亚大学举行。

The proposed workshop will provide a forum that promotes the interaction of researchers in the areas of wavelets and splines. While the study of spline functions is a well established subject of investigation, which has become an interdisciplinary research area during the past three or four decades, the subject of wavelets was born only about twenty years ago. However, the only known compactly supported functions with analytical formulation that generate a multiresolution approximation are the cardinal B-splines. Furthermore, the B-spline refinement symbols play the central role in the construction of Daubechies' wavelets, by assuring the convergence of certain infinite products that constitute the Fourier transform of the Daubechies scaling functions and the order of smoothness of these functions, as building blocks of the MRA's. This close relationship between splines and wavelets is the root of the need for the interaction between these two interdisciplinary areas of mathematical research. This conference on the interaction between wavelets and splines will bring together the leading experts of these two fields to exchange ideas, assess the state-of-the-art, and define the trends of future research problems that benefit both interdisciplinary areas. What is more important is that such a conference will be greatly beneficial to the young reserchers and the under-previleged groups, who would have very limited opportunities, if any at all, to interact with the leading experts of both subjects under the same roof. This proposed concerence will take place in the University of Georgia from 16-19, 2005.