Constructive Approximation and Harmonic Analysis

构造近似和调和分析

• 批准号: 1613790
• 负责人: Vladimir Temlyakov
• 金额: $ 2.63万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-03-15 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613790&HistoricalAwards=false
• 关键词: Constructive; Approximation; Harmonic; Analysis

This award provides funding to defray expenses of US-based participants (both young researchers and established scientists) in the intensive research program "Constructive Approximation and Harmonic Analysis", which is to be held at the Centre de Recerca Matematica (CRM) in Barcelona, Spain during the period of March-July, 2016. This program will concentrate on the areas of harmonic analysis and approximation theory, areas of mathematics that underlie the representation and approximation of functions and data. The emphasis will be put on constructive high-dimensional methods of approximation and representation. Recently, driven by applications in engineering, biology, medicine, and other areas of science, new challenging problems have appeared. A common feature of many of these problems is that they involve data and multivariable functions in extremely high dimensions, in which setting classical methods of approximation do not work well. This is an important and rapidly developing area of mathematics. A recent increase of activity at the interface of harmonic analysis and approximation theory makes the timing perfect for a research program that emphasizes this interplay and will help the cross fertilization of both fields. CRM is a renowned mathematics research institute which provides excellent facilities for such a program, and both harmonic analysis and approximation theory have historically been strongly represented in the activities of CRM.The program will include a workshop on "Function Spaces and High-Dimensional Approximation" (May 2016), several advanced courses on "Methods of Constructive Approximation and Harmonic Analysis" aimed at graduate students and postdocs (May-June 2016), and a Conference on "Harmonic Analysis and Approximation Theory" (HAAT 2016, June 2016). In addition there will be ample time for collaborative research. The program will bring together different groups of mathematicians working in several areas of analysis and numerical analysis to try to make a breakthrough in high-dimensional problems, which are very important in data compression and processing (critical to information technology applications and medical imaging). Progress in this area will impact several other mathematical sciences communities, including signal and image processing, numerical mathematics, learning theory, and optimization theory. The schedule of the events in the program has been carefully coordinated with other European and US events in these fields, which will allow a large number of US-based mathematicians to participate. The web site for the conference is http://www.crm.cat/en/Activities/Curs_2015-2016/Pages/IRP-Approximation-and-Harmonic-Analysis.aspx

该奖项提供资金，以支付美国参与者（包括年轻研究人员和知名科学家）在密集的研究计划“建设性近似和谐波分析”中的费用，该计划将于2016年3月至7月期间在西班牙巴塞罗那的Centre de Recerca Matematica（CRM）举行。 该计划将集中在谐波分析和近似理论，数学领域的基础上的表示和函数和数据的近似领域。 重点将放在建设性的高维近似和表示方法。 近年来，在工程、生物、医学和其他科学领域的应用的推动下，出现了新的挑战性问题。 许多这些问题的一个共同特点是，它们涉及数据和多变量函数在极高的维度，其中设置经典的近似方法不工作。 这是数学中一个重要而迅速发展的领域。 最近在调和分析和近似理论的接口活动的增加，使得时间完美的研究计划，强调这种相互作用，并将有助于这两个领域的交叉施肥。 CRM是一个著名的数学研究机构，为这样一个计划提供了良好的设施，调和分析和逼近理论在CRM的活动中一直很有代表性。该计划将包括一个关于“函数空间和高维逼近”的工作坊。（2016年5月），几门针对研究生和博士后的“构造性近似和调和分析方法”高级课程（2016年5月至6月），以及关于“谐波分析和近似理论”的会议（HAAT 2016，2016年6月）。 此外，将有足够的时间进行合作研究。 该计划将汇集在分析和数值分析的几个领域工作的不同数学家群体，试图在高维问题上取得突破，这在数据压缩和处理中非常重要（对信息技术应用和医学成像至关重要）。 这一领域的进展将影响其他几个数学科学社区，包括信号和图像处理，数值数学，学习理论和优化理论。 该计划中的活动时间表已与这些领域的其他欧洲和美国活动进行了精心协调，这将使大量美国数学家参加。 会议的网址是http://www.crm.cat/en/Activities/Curs_2015-2016/Pages/IRP-Approximation-and-Harmonic-Analysis.aspx