Composition Operators (Mathematics)

MacCluer博士的研究是算子理论和函数理论的结合。这些问题涉及解析函数空间上复合算子研究的各个方面，并包括与Carl Cowen （Purdue University）共同研究确定作用于CN， n1的单位球BN上解析函数的Hilbert空间上的复合算子的谱问题的延续。研究了这样一个Hilbert空间的自同态不变性现象，以及它与复合算子问题的联系。此外，还继续与Thomas Kriete（弗吉尼亚大学）合作研究圆盘上大加权Bergman空间上的复合算子，并继续MacCluer等人最近关于BN上解析函数空间上复合算子的基本性质的工作。N 1。在主办机构的互动活动包括：教授一学期的研究生水平课程，该课程基于普渡大学主办机构麦克卢尔博士和卡尔·考恩撰写的关于作文操作符的书。此外，将在普渡大学的研讨会和沃巴什现代分析研讨会上进行客座讲座。麦克卢尔博士还将寻找机会与本科生和研究生以各种方式进行互动，包括非正式的和结构化的。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

Dr. MacCluer's research lies at the interface of operator theory and function theory. These problems involve aspects of the study of composition operators on analytic function spaces, and include a continuation of joint work with Carl Cowen (Purdue University) on the question of identifying the spectrum of a composition operator acting on a Hilbert space of analytic functions on the unit ball BN of CN, N 1. A study of the phenomena of auotmorphism invariance of such a Hilbert space, and its connection with composition operator questions will be pursued. Additionally, there is continuing joint work with Thomas Kriete (University of Virginia) on a study of composition operators on large weighted Bergman spaces on the disc, and a continuation of recent work of MacCluer and others on basic properties of composition operators on spaces of analytic functions on BN, N 1. Interactive activities at the host institution include: teaching a one semester graduate level course based on a book being written by Dr. MacCluer and Carl Cowen at Purdue-the host institution-on composition operators. Additionally, guest lectures in seminars at Purdue and at the Wabash Modern Analysis Seminar will be given. Dr. MacCluer will also seek out opportunities for interaction with both undergraduate and graduate students in a variety of ways, both informal and structured. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.