Constructive Approximation and Harmonic Analysis

该奖项提供资金，用于支付美国参与者(包括年轻研究人员和知名科学家)的费用，该项目将于2016年3-7月在西班牙巴塞罗那的Matematica中心(CRM)举行，该密集研究项目将于2016年3月至7月在西班牙巴塞罗那举行。本课程将集中于调和分析和近似理论领域，这些领域是函数和数据表示和近似的基础数学领域。重点将放在构造性高维近似和表示方法上。近年来，在工程、生物、医学等科学领域应用的推动下，出现了新的挑战性问题。其中许多问题的一个共同特征是，它们涉及极高维度的数据和多变量函数，在这种情况下，设置经典的近似方法不能很好地发挥作用。这是一个重要且发展迅速的数学领域。最近，调和分析和近似理论交界处的活跃度增加，为强调这种相互作用的研究计划提供了完美的时机，并将有助于这两个领域的交叉受精。CRM是一家著名的数学研究机构，为这一项目提供了极好的设施，调和分析和逼近理论在CRM的活动中历来都有很强的代表性。该项目将包括一个关于“函数空间和高维逼近”的研讨会(2016年5月)，几个针对研究生和博士后的关于“构造逼近和调和分析的方法”的高级课程(2016年5月至6月)，以及一个关于“调和分析和逼近理论”的会议(HAAT 2016,2016年6月)。此外，还将有充足的时间进行合作研究。该计划将汇集在几个分析和数值分析领域工作的不同数学家群体，试图在高维问题上取得突破，这些问题在数据压缩和处理(对信息技术应用和医学成像至关重要)中非常重要。这一领域的进展将影响其他几个数学科学界，包括信号和图像处理、数值数学、学习理论和最优化理论。该项目的活动日程与欧洲和美国在这些领域的其他活动进行了仔细的协调，这将允许大量在美国的数学家参与。会议的网址是http://www.crm.cat/en/Activities/Curs_2015-2016/Pages/IRP-Approximation-and-Harmonic-Analysis.aspx。

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