Operator algebras of multipliers on reproducing kernel Hilbert spaces

我的研究项目的目的是对被称为运算符的数学对象进行分类。运算符是一种具有非常严格的性质的变换，称为线性。例如，绘制作用在笛卡尔平面上的线性变换的图形会产生三维空间中的另一个平面。运算符的这种简单性质使它们易于使用数学工具进行分析。另一方面，运算符可以有效地用于描述自然科学和工程中发生的许多重要现象。事实上，它们是例如出现在量子力学中的基本物体。因此，有必要为它们发展一套坚实的数学理论。我的研究得出的预期分类将为理解运算符提供一种方便的方法，并可能使其他领域的数学家和科学家受益。

The aim of my research program is to classify mathematical objects called operators. An operator is a transformation having a very rigid property known as linearity. Plotting the graph of a linear transformation acting on the Cartesian plane results in another plane in three dimensional space, for instance. This simple property of operators makes them amenable to analysis using mathematical tools. On the other hand, operators can be fruitfully used to describe many important phenomena occurring in natural science and engineering. Indeed, they are the basic objects appearing in quantum mechanics for example. Consequently, it is desirable to develop a solid mathematical theory for them. The anticipated classification resulting from my research would yield a convenient method for understanding operators, and could benefit both mathematicians and scientists in other fields.