Mathematical Sciences: Some Elementary Inequalities

班尼特教授将继续他对“初等不等式”的研究，即那些涉及非负项矩阵的不等式。主要目标是找到序列空间之间各种矩阵变换的范数估计。应用于概率论、函数论、正交级数和一般不等式理论。工作层面的数学分析通常是对不等式的巧妙处理。例如，有一个著名的不等式，它断言两个正数序列的乘积之和不大于第一个序列的平方和乘以第二个序列的类似表达式的平方根。这个事实和无数其他类似的事实构成了分析论证的基本信息。班尼特教授的研究旨在从根本上丰富这一事实储备。

Professor Bennett will continue his research on "elementary inequalities," i.e. those involving matrices with non-negative entries. The main objective is to find norm estimates for various matrix transformations between sequence spaces. Applications are to probability theory, function theory, orthogonal series, and the general theory of inequalities. Mathematical analysis at the working level is often a matter of the ingenious manipulation of inequalities. For instance, there is a famous inequality asserting that the sum of products of two sequences of positive numbers is not greater than the square root of the sum of squares of the first sequence times the analogous expression for the second. This fact and countless others like it constitutes the basic information out of which analytic arguments are spun. The research of Professor Bennett aims at fundamental enrichment of this store of facts.