Fourier analysis and partial differential equations

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。Fefferman一直致力于寻找有效的算法，通过“几乎尽可能平滑”的插值函数来插入多维数据（在引号中的短语的各种解释下）；并研究表面QG方程（二维不可压缩流体方程）可能的自相似击穿场景。Stein一直致力于寻找一般定理，保证在几个复杂变量中产生的相关算子在适当的函数空间上有界。他还致力于开发涉及随机波动的基本模型的股票价格分布的渐近性。费弗曼：在科学和技术的许多目的中，数据的插值是很重要的。（几乎）不可压缩的流体在自然界中存在，但人们对它们如何流动几乎没有基本的了解。Stein：用于研究函数空间算子的调和分析方法在理解各种科学技术现象方面有着广泛的应用。在更好地理解随机微分方程解的性质方面也有很大的用处。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Fefferman has been working to find efficient algorithms to interpolate multidimensional data by an interpolating function that is "nearly as smooth as possible" (under various interpretations of the phrase in quotes); and investigating a possible self-similar breakdown scenario for the surface QG equation, an incompressible fluid equation in 2 space dimensions. Stein has been working on finding general theorems that guarantee that relevant operators arising in several complex variables are bounded on appropriate function spaces. He has also been working to develop the asymptotics of stock-price distributions for basic models involving stochastic volatility. Fefferman: Interpolation of data is important for many purposes in science and technology. (Nearly) incompressible fluids occur in nature, but there is little fundamental understanding of how they flow.Stein: Methods of harmonic analysis used in studying operators on function spaces have vast applications in understanding a variety of phenomena in science and technology. There is also great utility in better understanding the nature of solutions of stochastic differential equations.