International Conference on Interpolation in Spaces of Analytic Functions at CIRM

CIRM 解析函数空间插值国际会议

• 批准号: 1936503
• 负责人: Brett Wick
• 金额: $ 1.2万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2020-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1936503&HistoricalAwards=false
• 关键词: International; Conference; Interpolation; Spaces; Analytic

The primary goal of this project is to provide participant support for graduate students, early-career, and/or mathematicians from underrepresented groups allowing them to attend the international conference on Interpolation in Spaces of Analytic Functions at the Centre de Rencontres Mathematiques (CIRM) in Marseille, France during the week of November 18-22, 2019. The 5-day conference will gather people interested in holomorphic interpolation and related subjects, including sampling theory, uniqueness problems, and reproducing kernel Hilbert spaces. There will be approximately 20 one-hour talks by prominent international mathematicians, many of them from the U. S., with interests related to interpolation and spaces of analytic functions. A problem session and additional contributed talks will also be part of the conference schedule. The organizers of the conference are committed to supporting the participation of women, minorities, and researchers. To facilitate their development as researchers and educators, it is extremely important to provide opportunities for the interaction between young mathematicians and established researchers. These interactions will be facilitated by the breaks and discussion sessions that will be part of the schedule.In the Hilbertian situation, interpolation, uniqueness, and sampling translate to geometric properties of reproducing kernels. After orthonormal sequences, Riesz sequences of such kernels (which are related to interpolation) represent the second-best family one can expect in a Hilbert space. Riesz sequences, and their complete counterpart, Riesz bases, are fundamental elements contributing not only to a better understanding of the underlying Hilbert spaces, but playing a central role in operator theory and its applications, such as signal processing, mathematical physics, and machine learning. We are particularly interested in the use of Riesz bases in control theory. We also note that in the last decade spectacular progress was made when several longstanding open problems were solved (e.g., the Kadison-Singer conjecture and the completeness problem for biorthogonal exponentials). The conference website can be found at: https://conferences.cirm-math.fr/2055.htmlThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的主要目的是为研究生，早期职业和/或数学群体提供参与者的支持，允许他们参加在2019年11月18日至22日，在2019年11月18日至22周的Marseille Impports of People the People of People of People of People。受试者，包括抽样理论，独特性问题和繁殖Hilbert空间。著名的国际数学家将大约有20个小时的谈判，其中许多来自美国，并具有与插值和分析功能空间有关的兴趣。 问题会议和其他贡献会议也将是会议时间表的一部分。 会议的组织者致力于支持妇女，少数民族和研究人员的参与。为了促进他们作为研究人员和教育工作者的发展，为年轻数学家和成熟研究人员之间的相互作用提供机会非常重要。 这些相互作用将通过将成为时间表的一部分的休息和讨论会来促进。在希尔伯特式的情况下，插值，独特性和采样将转化为复制核的几何特性。在正顺序序列之后，此类内核的Riesz序列（与插值相关）代表了人们在希尔伯特空间中可以期望的第二好家族。 Riesz序列及其完整的对应物Riesz基础是基本要素，不仅有助于更好地了解基础希尔伯特空间，而且在操作员理论及其应用中起着核心作用，例如信号处理，数学物理学和机器学习。我们对在控制理论中使用Riesz碱特别感兴趣。我们还注意到，在过去的十年中，当解决了几个长期的开放问题时（例如，Kadison-Singer的猜想和生物双歧指数的完整性问题），取得了壮观的进步。会议网站可以在以下网站上找到：https：//conferences.cirm-math.fr/2055.htmlthis Award反映了NSF的法定任务，并且使用基金会的知识分子和更广泛的影响评估标准，认为值得通过评估来获得支持。