Mathematical Sciences: Problems in Operator Theory and Related Areas

Bercovici教授将研究凸平面上测度的自由加性和乘法卷积的性质，以及这些运算在谱不变量计算中的应用。他将继续研究Nevanlinna-Pick、Caratheodory和Nehari问题的光谱版本，并探索它们与控制理论的关系。另一个研究课题是对偶代数的结构，重点是由有限个交换算子生成的代数。Bercovici教授的研究涉及希尔伯特空间的算子。希尔伯特空间算子本质上是复数的无限矩阵。这些运算符在应用科学的各个领域以及纯数学中都有应用。这类研究是试图对这类算子的某些重要族进行分类。

Professor Bercovici will study the properties of free additive and multiplicative convolution of measures in the convex plane, as well as applications of these operations to the calculation of spectral invariants. He will continue the study of spectral versions of the Nevanlinna-Pick, Caratheodory, and Nehari problems and explore their relations with control theory. Another topic of study will be the structure of dual algebras with an emphasis on algebras generated by a finite number of commuting operators. Professor Bercovici's research concerns operators on Hilbert space. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. Research of this type is an attempt to classify certain important families of such operators.