Mathematical Sciences: Problems in Linear Analysis

数学科学：线性分析问题

• 批准号: 9500924
• 负责人: Leiba Rodman
• 金额: $ 12万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500924&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Linear; Analysis

PROPOSAL NO.: DMS - 9500924 PROPOSAL TITLE: Problems in Linear Analysis PI/PD: Leiba Rodman CO-PI/PD: Hugo J. Woerdeman ABSTRACT The principal investigators plan to study a variety of interconnected problems in a highly active area of research in Mathematical Sciences that involves operator theory, matrix analysis, and their applications in science and technology, using also closely related areas of pure and applied mathematics: function theory, Fourier analysis. In addition to continuing work on other topics, specific problems are outlined in the following subjects which are the main focus of the research: 1. Interpolation problems for matrix and operator valued functions; 2. Completions of finite and infinite matrices and operators; 3. Riccati equations; 4. Krein space operators; 5.Applications. The principal investigators strive to develop new results that can be proved in an abstract mathematical context (e. g., in terms of *-algebras), and that at the same time yield new and useful information in various more specific settings. The principal investigators plan to relate the newly obtained abstract results to the original areas of application. Applications that are emphasized in the proposal include Advanced Manufacturing (engineering control systems) and High Performance Computing and Communications (tomography), which have been identified as two of the strategic areas with impact on national need. Other areas of relevant application are: engineering control systems, optics of polarized light, kinetic energy minimization in quantum chemistry, diffraction of waves, signal processing, and pattern recognition. Interactions with many researchers in different fields (mathematics, computer science, engineering), various countries besides the U. S. (Canada, The Netherlands, Italy, Israel, Norway, France, United Kingdom), and scientists in industry and government (the National Institute of Health, NEC Research Institute) are planned and form an integral part of this project.

提案编号：DMS - 9500924 提案标题：线性分析中的问题 PI/PD：Leiba Rodman CO-PI/PD：Hugo J. Woerdeman 摘要 主要研究人员计划研究高度活跃的研究领域中的各种相互关联的问题。数学科学，涉及算子理论、矩阵分析及其在科学和技术中的应用，还使用与纯数学和应用数学密切相关的领域：函数论、傅里叶分析。除了继续研究其他主题外，还概述了以下主题中的具体问题，这些主题是研究的主要焦点： 1. 矩阵和算子值函数的插值问题； 2. 有限和无限矩阵和运算符的补全； 3.黎卡提方程； 4. Kerin空间算子； 5.应用。主要研究人员努力开发新的结果，这些结果可以在抽象的数学背景下（例如，在 *-代数方面）得到证明，同时在各种更具体的环境中产生新的有用的信息。 主要研究人员计划将新获得的抽象结果与原来的应用领域联系起来。该提案强调的应用包括先进制造（工程控制系统）和高性能计算和通信（断层扫描），这两个领域已被确定为影响国家需求的两个战略领域。 其他相关应用领域包括：工程控制系统、偏振光光学、量子化学中的动能最小化、波衍射、信号处理和模式识别。 与不同领域（数学、计算机科学、工程学）、美国以外的各个国家（加拿大、荷兰、意大利、以色列、挪威、法国、英国）以及工业和政府科学家（美国国家研究院）的许多研究人员进行互动Health、NEC 研究所）已规划并构成该项目的组成部分。