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

该奖项将支持波士顿马萨诸塞大学的James Byrnes博士和新南威尔士大学的Gavin Brown博士之间的合作研究。本研究旨在促进对限制系数三角和性质的理论认识，并探索这些结果在重要工程问题中的应用。该项目的一个主要焦点是解决多项式的模量在曲线上（通常是单位圆）有多接近常数的问题，在这种情况下，多项式是一个有限三角函数和。这个问题对理论数学分析很重要，因为多项式的基本性质，对工程也很重要，因为它适用于发射机设计中最小化峰值与平均功率比的问题。该项目代表了美国和澳大利亚研究人员之间的卓越合作，因为双方都在扩展他们在经典数学分析方面的并行专业知识，以解决工程问题，这对两国都很重要。这是数学研究中一个重要领域的重要基础工作，同时也具有解决重大工程问题的潜力。

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.