Certain C*-Algebras of Toeplitz Operators and Singular Integral Operators

Toeplitz 算子和奇异积分算子的某些 C* 代数

• 批准号: 9400600
• 负责人: Jingbo Xia
• 金额: $ 4万
• 依托单位: SUNY at Buffalo
• 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: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400600&HistoricalAwards=false
• 关键词: Certain; Algebras; Toeplitz; Operators; Singular

9400600 Xia The investigation will examine the structure of C*-algebras generated by Toeplitz operators and singular integral operators associated within-dimensional flows. This class of C*-algebras includes many classical examples. The investigation is particularly directed to the case where n is greater than 1. In this case each algebra contains a chain of ideals that will be analyzed carefully. These ideals will be used to compute K- groups, which are important invariants for the classification of C*-algebras. The k-groups will also be used to study the invertibility of systems of Toeplitz operators. In this connection an attempt will be made to determine the stable rank of certain commutator ideals. An analysis will be made of certain automorphisms of the Toeplitz algebra on the unit circle which are induced by homeomorphisms of the circle. This project investigates certain algebras generated by classical operators that arise from the study of singular integral equations. These equations can be traced back to applications in engineering and manufacturing such as the equation of the airfoil and the stamping of metal plates. The abstract problem here is the classification of these algebras using invariants. The contributions will be to many fields of pure mathematics including ergodic theory, analysis and geometry. ***

小行星9400600 研究由Toeplitz算子和奇异积分算子生成的C*-代数的结构。这类C*-代数包括许多经典的例子。研究特别针对n大于1的情况。在这种情况下，每个代数都包含一个理想链，将仔细分析。这些理想将被用来计算K-群，它们是C*-代数分类的重要不变量。k-群也将用于研究Toeplitz算子系统的可逆性。在这方面，将试图确定某些交换子理想的稳定秩。分析了单位圆上Toeplitz代数的某些自同构，它们是由圆的同胚所诱导的。 本计画研究由奇异积分方程研究中所产生的古典算子所产生的某些代数。这些方程可以追溯到工程和制造中的应用，例如机翼方程和金属板的冲压。这里的抽象问题是使用不变量对这些代数进行分类。贡献将是许多领域的纯数学，包括遍历理论，分析和几何。 ***