Composition Operators (Mathematics)

MacCluer博士的研究处于算子理论的界面 功能理论。 这些问题涉及到研究的方方面面 解析函数空间上的复合算子，包括 继续与卡尔·考恩（普渡大学）合作， 识别复合算子谱的问题 作用在单位球BN上解析函数的Hilbert空间上 CN，N 1。 自态不变性现象的研究 这样一个希尔伯特空间，它与复合的联系， 操作员的问题将继续进行。 此外还有 继续与托马斯Kriete（弗吉尼亚大学）合作 关于大加权Bergman上复合算子的研究 光盘上的空间，并继续最近的工作MacCluer 等关于空间上复合算子的基本性质 BN上的解析函数，N 1。 主办机构的互动活动包括： 一个学期的研究生水平的课程，根据一本书正在写 麦克卢尔博士和卡尔考恩在普渡大学-主办机构-对 复合运算符 此外，还在下列地点的研讨会上进行客座讲座： 普渡大学和瓦巴什现代分析研讨会将给予。 MacCluer博士还将寻求与 无论是本科生还是研究生， 非正式和结构化。 本项目进一步促进了VPW计划的目标，即（1） 为妇女提供机会， 工程和科学的学科由NSF支持， (2)鼓励女性从事科学和工程职业 通过提高女性科学家和工程师的知名度， 受雇于工业、政府和学术机构。 通过 鼓励妇女参与科学，这是一个宝贵的 投资于国家未来的科学活力。

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.