Matrix-like Representations in Time-Frequency and Applied Harmonic Analysis

Northern Illinois University, Dekalb IL

Investigators

Abstract

Krishtal DMS-0908239 The project is dedicated to creation, development, and application of a unified theory of matrix-like representations for frames, fusion frames, and fuzzy fusion frames; and causality theory and regular factorizations of pseudodifferential operators. These topics touch upon a large variety of areas of fundamental and applied analysis, including frame theory, pseudodifferential operator theory, Banach modules and representations of locally compact Abelian groups, non-standard multiresolution analysis, and signal processing. The problems studied in this project address interesting and important questions regarding certain mathematical tools on which modern signal processing is based. The project is also expected to lead to new questions in more fundamental analysis, thus promoting cross-fertilization of the fields. The investigator and his colleagues develop a mathematical framework aimed to address various problems posed by the deluge of data in the modern world. Potential applications include image processing, wireless communications, and others. Particular attention is given to an application for proton computed tomography. Broader impact of the proposed activities includes integration of research and education, dissemination of knowledge, and enhancement of interdisciplinary collaboration, both domestic and international.