Composition Operators (Mathematics)

麦克卢尔博士的研究位于算子论和函数论的交界处。这些问题涉及解析函数空间上复合算子研究的方方面面，包括与普渡大学的Carl Cowen在Cn，N1的单位球BN上作用于解析函数的Hilbert空间上的复合算子的谱的识别问题的继续工作。我们将继续研究这种Hilbert空间的自同构不变性现象，以及它与复合算子问题的联系。此外，继续与Thomas Kriete(弗吉尼亚大学)合作研究圆盘上大型加权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，主办机构的互动活动包括：根据主办机构普渡大学的麦克克鲁尔博士和卡尔·考恩正在撰写的一本关于作文运算符的书，教授一学期的研究生课程。此外，还将在普渡大学的研讨会和瓦巴什现代分析研讨会上进行客座讲座。麦克卢尔博士还将通过各种方式寻找与本科生和研究生互动的机会，包括非正式的和有组织的。该项目进一步推动了VPW计划的目标，即：(1)为妇女提供机会，在NSF资助的工程和科学学科中发展她们的职业生涯；(2)通过提高受雇于工业、政府和学术机构的女科学家和工程师的知名度，鼓励妇女追求科学和工程事业。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.