Mathematical Sciences: Bilinear Problems in Analysis

小行星9423678 双线性算子是调和分析和遍历理论中的一个非常困难的问题。当前项目的一个主要焦点是双线性希尔伯特变换。特别是，调查员将研究困难的问题，卡尔德龙涉及平方可积的价值，这一转变。该方法将涉及遍历和傅立叶变换技术的合成。 数学分析包括对方程解的定性和定量信息的研究。通常，真实的世界方程可以被看作是算子方程，并且解的分析涉及对算子的全局和局部估计。这个项目涉及双线性算子的值估计，即与函数对相关的算子。这些困难的分析问题的方法将涉及几个深入的分析分支的综合。

9423678 Lacey Bilinear operators are a source of very difficult questions in harmonic analysis and ergodic theory. A major focus in the current project is the bilinear Hilbert transform. In particular, the investigator will study the difficult problem of Calderon involving the square integrability of the value of this transform. The approach will involve a synthesis of ergodic and Fourier transform techniques. Mathematical analysis involves the study of qualitative and quantitative information about solutions of equations. Frequently, real world equations can be viewed as operator equations and the analysis of solutions involves estimates on operators both globally and locally. This project involves estimation on the value of bilinear operators, that is, operators associated with pairs of functions. The approach to these difficult analytical questions will involve a synthesis of several deep branches of analysis.