DMS-9500235 de Souza/Brown This award will continue to partially a program that has sponsored two mini-conferences on real and harmonic analysis a year since 1986. These conferences are held at Auburn University, and attracts participants primarily form the southeastern states. These meetings have enjoyed a steady increase in level of participation and served as a stimulant for activity in both the geographic and academic area. Harmonic analysis combines those elements of mathematics best exemplifying the ideas of synthesis. One seeks to decompose complex problems into fundamental components. These components are then analyzed for their basic characteristics. Finally, the solution is reconstructed through a recombination of the components. The Fourier series and Fourier transform are examples of tools used in this context; one discrete , the other representing a continuous decomposition. More recently the theory of oscillatory integrals added new dimensions to some of the more classical approaches to harmonic analysis.
