U.S.-Romania Mathematics Research: Factorization, Extension, and Interpolation Problems for Operator-valued Functions on Groups

美国-罗马尼亚数学研究：群上算子值函数的因式分解、可拓和插值问题

• 批准号: 0307395
• 负责人: Mihai Bakonyi
• 金额: $ 2.81万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0307395&HistoricalAwards=false
• 关键词: U.S.; Romania; Mathematics; Research; Factorization

The goal of this U.S.-Romanian mathematics project between Mihai Bakonyi of Georgia State University and Dan G. Timotin of the Romanian Academy's Institute of Mathematical Sciences is to advance our knowledge of positive definite functions on groups, an area of interest in noncommutative harmonic analysis. This will be accomplished by considering two classes of groups, first, totally ordered abelian groups and second, finitely generated nonabelian free groups. Building on the U.S. participants' strengths in factorization and extension problems and the Romanian side's in interpolation and operator generalizations, the team intends to examine: 1) factorization of positive definite operator-valued functions, 2) extensions of partially positive definite operator-valued functions on finitely generated free groups and 3) interpolation of operator-valued functions on free groups. Results are expected to lead to a more unified theoretical framework for multivariable operator theory and related areas of operator algebras. Success would enhance future applications in system theory and electrical engineering. This mathematics project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence. Broader impacts include the introduction of U.S. and Romanian students to the international community of people working on multivariable operator theory through collaborative work at partner institutions and direct involvement in the project's advanced data analysis and modeling techniques.

美国的目标是-罗马尼亚格鲁吉亚州立大学的Mihai Bakonyi和Dan G.罗马尼亚科学院数学科学研究所的研究生项目是为了提高我们对群上正定函数的认识，这是非对易调和分析的一个感兴趣的领域。这将通过考虑两类群来实现，第一，全序阿贝尔群，第二，非阿贝尔生成的自由群。 基于美国参与者在因式分解和扩展问题方面的优势以及罗马尼亚方面在插值和算子推广方面的优势，该团队打算研究：1）正定算子值函数的因式分解，2）部分正定算子值函数在自由群上的扩展，以及3）自由群上算子值函数的插值。 结果预计将导致一个更统一的理论框架，多变量算子理论和相关领域的算子代数。 这一成功将促进未来在系统理论和电气工程中的应用。这个数学项目实现了促进科学知识的计划目标，使美国和中欧的专家能够联合收割机互补人才，并在共同感兴趣和能力强的领域共享研究资源。 更广泛的影响包括将美国和罗马尼亚学生介绍给国际社会的人们，他们通过在合作机构的合作工作和直接参与该项目的先进数据分析和建模技术来研究多变量算子理论。