9530310 Ehrenpreis This award provides support for a conference on applications of harmonic analysis in number theory and approximation theory. The conference is being held in honor of Donald J. Newman, and the emphasis is on areas of mathematics that have been influenced by Newman's ideas. The conference will create opportunities for cross-fertilization of ideas among workers in two important areas of classical mathematics. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems. 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. Harmonic analysis is a surprisingly useful tool in studying whole numbers.
