An Operator Approach to Problems in Analysis and Probability: Matrix Muckenhoupt Weights, Hankel and Toeplitz Operators, Singular Integrals and the Angle between Past and Future

分析和概率问题的算子方法：矩阵 Muckenhoupt 权重、Hankel 和 Toeplitz 算子、奇异积分以及过去与未来之间的角度

• 批准号: 9622936
• 负责人: Serguei Treil
• 金额: $ 12.13万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622936&HistoricalAwards=false
• 关键词: Operator; Approach; Problems; Analysis; Probability

Abstract Treil/Volberg DMS-9622963 Treil and Volberg will continue their research on bases of classical wavelets in vector weighted spaces. They will consider some classical problems in the theory of Hankel and Toeplitz operators in spaces of analytic functions, singular integral operators. One goal is the generalizations of these problems to multi-parameter (vector) setting. Other problems they will investigate are Sarason's problem about necessary and sufficient condition for a product of two (unbounded) Toeplitz operators to be bounded, description of completely regular multivariate stationary Gaussian processes, two weights inequality for Bergman Projection, and boundedness of a product of two (big) Hankel operators in the Bergman space. Singular integrals is one of the main tools analysis brought to applications (signal processing, market models, prediction theory, etc..). In practice many such problems have a vector (multi-parameter) nature. The proposed research is based on the approach targeting exactly the multi-parameter nature of such problems and overcomes the difficulty stemming from this multi-parameter nature. Among the practical applications of the research are prediction theory for stationary Gaussian processes, wavelets (signal processing). The authors strongly feel that the developed technique can be helpful.

摘要Treil/Volberg DMS-9622963 Treil和Volberg将继续对矢量加权空间中经典小波的研究进行研究。 他们将在分析函数，单数积分运算符的空间中考虑Hankel和Toeplitz运营商理论中的一些经典问题。 一个目标是将这些问题概括为多参数（向量）设置。 他们将研究的其他问题是萨拉森（Sarason）关于两个（无限）托管操作员的必要条件和足够条件的问题，描述了完全常规的多元多元固定式高斯流程，伯格曼投影的两个权重不平等以及伯格曼空间中两个（大）汉克尔运营商的产品的界限。 单数积分是带给应用程序（信号处理，市场模型，预测理论等）的主要工具分析之一。实际上，许多这样的问题具有矢量（多参数）性质。 拟议的研究是基于针对此类问题的多参数性质的方法，并克服了这种多参数性质的难度。 研究的实际应用包括固定高斯过程，小波（信号处理）的预测理论。作者强烈认为开发的技术可能会有所帮助。