US-France Cooperative Research: Polynomials with Concen- tration at Low Degrees and Applications

该奖项将支持肯特州立大学Richard Varga博士、Per Enflo博士和法国巴黎第七大学微积分研究所Bernard Beauzamy教授在计算数学方面的合作研究。一个重要的新概念最近被dr。Beauzamy和Enflo关于多项式的浓度。数学的许多领域都涉及到多项式的估计，这些估计涉及到多项式的程度。例如，在谐波分析、数论和近似理论中就会出现这种情况。这个项目的目的是获得多项式的类似估计，现在只依赖于这些多项式的浓度，而不是它们的程度。这项工作的一个应用将是延森公式在函数理论中的推广。该项目将受益于研究人员在巴拿赫空间和数值分析方面的互补专业知识，以及法国小组的特殊理论实力。

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.