Mathematical Sciences: Topics in Operator Theory

数学科学：算子理论专题

• 批准号: 9401848
• 负责人: Ilya Spitkovsky
• 金额: $ 6.75万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401848&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Operator; Theory

9401848 Spitkovsky The project involves work on operator theory and matrix theory. Five specific projects are outlined: 1. Fredholm theory of Toeplitz, Weiner-Hopf and pseudodifferential operators on spaces with general Hunt-Muckenhoupt-Wheeden weights. Almost periodic factorization of matrix functions and its applications to extension and interpolation problems of Analysis. 3. Explicit solutions of integral equations and boundary problems emerging from applications to diffraction theory, elasticity and thermodynamics. 4. Further analysis of the structure of Banach algebras generated by two projections. 5. Contragredient canonical forms of pairs of Hermitian matrices and their applications. The project centers around the theory of systems of singular integral equations. Historically, these equations grew out of the study of the equation of the airfoil and other applications in the mechanics of materials. The basic tool for solving these singular integral equations is the method of Wiener-Hopf factorization. The matrix form of this factorization was developed independently by electrical engineers to study linear systems theory. A part of the project deals with explicit factorization and this would have application in engineering problems. When completed, the theoretical portion of the project will be a significant advance in the theory of matrix function factorization. ***

9401848斯皮特科夫斯基该项目涉及算子理论和矩阵理论方面的工作。1.具有一般Hunt-Muckenoupt-Wheeden权的空间上Toeplitz算子、Weiner-Hopf算子和伪微分算子的Fredholm理论。矩阵函数的概周期分解及其在分析的延拓和内插问题中的应用。3.在绕射理论、弹性力学和热力学中的应用中出现的积分方程和边值问题的显式解。4.进一步分析了由两个投影生成的Banach代数的结构。5.厄米特矩阵对的逆标准型及其应用。该项目以奇异积分方程组理论为中心。从历史上看，这些方程源于对翼型方程的研究和材料力学中的其他应用。求解这些奇异积分方程组的基本工具是Wiener-Hopf分解法。这种因式分解的矩阵形式是由电气工程师为研究线性系统理论而独立开发的。该项目的一部分涉及显式因式分解，这将在工程问题中应用。完成后，该项目的理论部分将是矩阵函数因式分解理论的重大进步。***