Mathematical Sciences: Some Elementary Inequalities

数学科学：一些基本不等式

• 批准号: 9112804
• 负责人: Grahame Bennett
• 金额: $ 5.2万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-01 至 1994-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9112804&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Elementary; Inequalities

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.

班尼特教授将继续他的研究“小学 不等式”，即涉及非负矩阵的不等式 条目 主要目标是找到范数估计， 序列空间之间的各种矩阵变换。 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， 对不平等的巧妙操纵。 比如说， 有一个著名的不等式断言乘积之和 两个正数序列的平均值不大于 第一个序列的平方和的平方根乘以 第二个类似的表达。 这一事实和无数 其他类似的信息构成了 分析的论点是旋转的。 班尼特教授的研究 旨在从根本上丰富这些事实。