报告题目: Recent Development of Wavelets on the Interval
时间：2018-11-29 10:00-11:00
地点：18-918
报告人：韩斌
Abstract: Though wavelets for numerical computing have been extensively studied for many years, there are several key problems unresolved yet. Two of them are: (1) Riesz wavelets that are orthogonal with respect to derivatives at different scale levels for small condition numbers. (2) Wavelet bases on the interval $[0,1]$ with simple structure to deal with different boundary conditions. In this talk we shall completely characterize derivative-orthogonal Riesz multiwavelets, present several examples using Hermite spline functions, and then apply them to the numerical solutions of differential equations. As the second related part of this talk, we shall discuss how to construct wavelets and framelets on the interval $[0,1]$ so that the wavelets can achieve different boundary conditions or high vanishing moments. This is a joint work with M. Michelle.The talk is based on the following work:
\begin{enumerate}\item[1.] B. Han and M. Michelle, Derivative-orthogonal Riesz wavelets in Sobolev spaces with applications to differential equations, \emph{Appl. Comput. Harmon. Anal.}, in press, (2017).
\item[2.] B. Han and M. Michelle, Construction of wavelets and framelets on a bounded interval, \emph{Anal. Appl.}, in press, (2018)
\item[3.] B. Han, Framelets and Wavelets: Algorithms, Analysis, and Applications. \emph{Applied and Numerical Harmonic Analysis}, Birkhauser/Springer, Cham, (2017).
\item[4.] B. Han, M. Michelle, and Y. S. Wong, Biorthogonal wavelets on bounded intervals with vanishing moments and polynomial reproduction, preprint (2018).
\end{enumerate}
报告人简介：韩斌，加拿大阿尔伯塔大学（University of Alberta ）数学与统计科学系教授，其研究领域主要包括：应用与计算哈密顿分析，小波分析，小波方法在计算机图形学、信号处理、图像处理、数值计算中的应用。曾作为Ingrid Daubechies教授的博士后在普林斯顿大学访问，以Alexander von Humboldt research fellowship身份与Wolfgang Dahmen教授（Leibniz奖获得者）开展合作研究，在顶级学术杂志上发表60多篇论文，且是两种学术刊物的编委。荣居近10年来世界上前170位数学家之列，并在小波、逼近论、应用与计算哈密顿分析方面的多个国际会议上做邀请报告。
