Vortrag: "Riesz Wavelets on Intervals with Applications to Differential Equations"

Abstract:

Wavelets on bounded domains are important in many applications such as images and differential equations. For image processing, the boundary wavelets must have high vanishing moments to reduce the boundary artifacts, while for numerical computing, the boundary wavelets must satisfy certain boundary conditions. Though wavelets for numerical computing have been extensively studied for many years, a general procedure still remains unknown for constructing Riesz multiwavelet bases on the interval [0,1] having vanishing moments and satisfying boundary conditions. In this talk we shall first discuss the general theory of Riesz wavelets on the real line. Then we shall propose a general method for adapting biorthogonal wavelets on the real line to construct Riesz wavelets on the interval [0,1] having vanishing moments or satisfying boundary conditions. Then we shall provide their several applications to numerical solutions of differential equations. This is a joint work with M. Michelle and Y. S. Wong.