Wavelets, Frames and Group Representations

点击翻译按钮获取中文摘要

Proposal Number: DMS-0200756PI: Eric WeberABSTRACTIn the past twenty years, wavelet theory has developedinto a fundamental area of mathematics and applied science.Intimately related are frame theory and sampling theory, allwith a connection to harmonic analysis. The proposedresearch will investigate group representations as a unifying theme since they appear in the settings of wavelet,frame, and sampling theory. The research of Weber will useexisting tools from functional and harmonic analysis, whilealso developing tools related to group cocycles and maximalabelian self adjoint algebras as models of these objects.The proposed research is theoretical in nature, though muchof it is motivated by problems in applied mathematics. Thegoal of the research of Weber is to establish a solidmathematical foundation of wavelet and frame theory. However,the research will potentially impact problems in appliedmathematics and signal processing, such as digital signal multiplexing, redundant communications and securecommunications.