Approximation with Exponential Sums.

One major accomplishment has been the devising of a very general theory for establishing the existence of a best approximation to an arbitrary function by an exponential sum of a given order. A second result was the creation of a mathematical theory and workable numerical methods for constructing best Chebyshev, least mean, and least squares approximations for a given completely monotonic function by sums of exponentials. Finally, the compilation and publication of a bibliograph for approximation with exponential sums by the principal investigator will undoubtedly be of enormous value to others working in this area.