This award will support collaborative research in computational mathematics between Dr. Richard Varga, and Dr. Per Enflo, Kent State University and Professor Bernard Beauzamy, Institute for Mathematical Calculus, University of Paris 7, France. An important new concept has been introduced recently by Drs. Beauzamy and Enflo concerning the concentration of a polynomial. There are many areas of mathematics which involve estimating polynomials, with these estimates involving the degree of the polynomial. This occurs, for example, in harmonic analysis, number theory and approximation theory. The aim of this project is to obtain similar estimates of polynomials, which now depend only on the concentration of these polynomials and not their degree. An application of this work would be to the extension of Jensen's formula in function theory. The project will benefit from the complementary expertise of the investigators in Banach spaces and numerical analysis, as well as the particular theoretical strength of the French group.
