U.S.-Australia Cooperative Research: Trigonometric Sums andTheir Applications to Engineering Problems

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This award will support collaborative research between Dr. James Byrnes of the University of Massachusetts at Boston and Dr. Gavin Brown of the University of New South Wales. The research is to advance theoretical understanding of the properties of trigonometic sums with restricted coefficients, and to explore the application of these results to important engineering problems. A primary focus of the project is to resolve the question of how close to constant the modulus of a polynomial can be along a curve, typically the unit circle, in which case, the polynominal is a finite trigonometric sum. This question is important both to theoretical mathematical analysis because of the fundamental nature of polynominals, and to engineering because of the applicability of the work to the problem of minimizing peak to average ratios of power in transmitter design. The project represents excellent collaboration between the U.S. and Australian researchers in that both are at the point of expanding their parallel expertise in classical mathe- matical analysis to the solution of engineering problems, important to both countries. This is significant fundamental work in an important area of mathematical research, as well as having the potential for solving major engineering problems.