Mathematical Sciences: Analysis on Spaces of Analytic Functions

复变量解析函数的理论（那些在幂级数中可展开的，所以粗略地说，是复数的极限）在一个多世纪以来丰富了所有的数学。这样的函数具有许多显著的性质，例如，它们在封闭曲线内各点的值完全由它们在曲线上的值决定。这类函数很容易聚集到希尔伯特空间中，而希尔伯特空间上的算子理论在专门化到这些解析函数的空间时就显得格外生动。研究人员将研究Hardy， Bergman和Dirichlet函数空间上的特定算子类，以及单位圆盘上有界解析函数的代数。

The theory of analytic functions of a complex variable (those that are expandable in power series, so roughly speaking the limits of complex polynomials) has enriched all of mathematics for over a century. Such functions enjoy many remarkable properties, for instance that their values at points inside a closed curve are determined completely by their values on the curve. It happens that such functions readily aggregate themselves into Hilbert spaces, and the theory of operators on Hilbert space gains extra vividness when specialized to these spaces of analytic functions. The investigators will study specific classes of operators on the Hardy, Bergman, and Dirichlet function spaces, as well as algebras of bounded analytic functions on the unit disc.