Wavelets, Frames and Group Representations

University Of Wyoming, Laramie WY

Investigators

Abstract

Proposal Number: DMS-0200756 PI: Eric Weber ABSTRACT In the past twenty years, wavelet theory has developed into a fundamental area of mathematics and applied science. Intimately related are frame theory and sampling theory, all with a connection to harmonic analysis. The proposed research 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 use existing tools from functional and harmonic analysis, while also developing tools related to group cocycles and maximal abelian self adjoint algebras as models of these objects. The proposed research is theoretical in nature, though much of it is motivated by problems in applied mathematics. The goal of the research of Weber is to establish a solid mathematical foundation of wavelet and frame theory. However, the research will potentially impact problems in applied mathematics and signal processing, such as digital signal multiplexing, redundant communications and secure communications.