Mathematical Sciences: Invariant Subspaces in some Banach of Analytic Functions

小行星9401027 Richter和Sundberg将研究不变的sbspace 解析乘法算子格 解析函数的Banach或Hilbert空间上的函数。的 空间，将被调查包括狄利克雷和 开单位圆盘上的Bergman空间，以及 复平面上更一般的域。这些不变量 子空间问题自然与 经典分析，如零集和唯一集的问题。在这些调查所涉及的新技术将是“极值函数”在不变的子空间。 算子理论是数学的一个分支，它处理有限矩阵的无限推广对象。通常，这些操作符可以在某些函数集合上实现为乘法。在这种形式下，不变子空间和分类问题与自然函数的存在性和插值问题有关。本计画将有助于分类问题及相关的具体函数存在性问题。 ***

9401027 Sundberg Richter and Sundberg will investigate the invariant sbspace lattices of the operator of multiplication by an analytic function on Banach or Hilbert spaces of analytic functions. The spaces that will be investigated include the Dirichlet and Bergman spaces on the open unit disc, as well as Hardy spaces of more general domains in the complex plane. These invariant subspace problems are related naturally to questions from classical analysis, such as questions about zero sets and sets of uniqueness. The new technique involved in these investigation will be that of "extremal functions" in invariant subspaces. Operator theory is that branch of mathematics that treats objects that are infinite generalizations of finite matrices. Frequently, these operators can be given realization as mutiplications on certain collections of functions. In this form the invariant subspace and classification problem are related to natural function existence and interpolation questions. This project will contribute to both the classification problem and the related concrete function existence problems. ***