U.S.-Croatia Mathematics Research on the Theory of Reproducing Function Systems

Washington University, Saint Louis MO

Investigators

Abstract

The goal of this U.S.-Croatian cooperative research project between Guido Weiss and Edward Wilson of Washington University and Hrvoje Sikic of the University of Zagreb is to strengthen the theoretical foundation required for reproducing function systems of square integrable functions. This will be accomplished by bringing together a team of senior and junior U.S. and Croatian mathematicians with complementary expertise to first reexamine the shift invariant spaces approach from an algebraic perspective and second, incorporate the idea of a filter. Thirdly, they will examine various applications of a recently developed unified approach for characterizing those functions of finite families of foundations for which an appropriate set of translations, dilations and modulations produce an analyzing and/or synthesizing system. Results are expected to refine the theoretical framework for the field of wavelets and reproducing function systems thereby allowing systems of great generality to be studied simultaneously. Success would enhance our ability to conduct highly accurate signal analyses and information transfer, with implications for statistical analysis and likely applications in communication networks, coding systems, information storage and retrieval, and analysis of satellite and medical imaging data. . This mathematics project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and South Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.