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的Richard Varga博士、Per Enflo博士和法国巴黎7大学数学微积分研究所的Bernard Beauzamy教授在计算数学方面的合作研究。Beauzamy博士和Enflo博士最近引入了一个重要的新概念，即多项式的浓度。数学中有许多领域涉及多项式的估计，这些估计涉及多项式的次数。例如，在调和分析、数论和近似论中都会出现这种情况。这个项目的目的是获得类似的多项式的估计，现在只依赖于这些多项式的集中度，而不是它们的次数。这项工作的一个应用将是函数论中Jensen公式的推广。该项目将受益于研究人员在Banach空间和数值分析方面的互补专业知识，以及法国小组的独特理论实力。

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.