Mathematical Sciences: Harmonic Analysis Methods in OperatorTheory and Modern Analysis

9401009伯克森研究试图发展一种广泛的抽象算符理论，以扩展调和分析在一般分析结构中的作用。在这个项目中，通过扩展变换方法的理论和范围，将把强大的调和分析方法运用到算子理论中。这些研究构成了一个肥沃的正在进行的基础研究计划，近年来已成功应用于许多学科。方向和主题将包括以下主流主题：傅里叶乘子的乘子理论和最大估计的转移；傅立叶乘子的小波分解；内插方法和转移；遍历理论；抽象谱分解。计划中的研究将寻求对数学应用的广泛统一概述。从历史上看，这种方法对量子物理学等学科至关重要，这些学科的解释依赖于广泛的抽象数学原理。***

9401009 Berkson The investigations seek to develop a broad abstract operator theory which expands the role of harmonic analysis in the structures of general analysis. In this program, the powerful methods of harmonic analysis will be harnessed to operator theory by expanding the theory and scope of transference methods. These investigations constitute a fertile ongoing program of fundamental research which has been successfully applied to numerous disciplines in recent years. The directions and themes will include the following mainstream topics: multiplier theory and transference of maximal estimates for Fourier multipliers; wavelet decompositions for Fourier multipliers; interpolation methods and transference; ergodic theory; abstract spectral decompositions. The planned research will seek a wide unified overview of mathematical applications. Historically such an approach is crucial to disciplines such as quantum physics, which rely for their explication on broad abstract principles of mathematics. ***