Mathematical Sciences: Operators on Dirichlet-Type Spaces

里克特教授将研究乘法的结构 一个广义Dirichlet空间上的z 他将试图 理解这个的不变子空间的结构 操作符. 当单位圆盘上的相应度量为 Lebesgue测度，则算子理论问题教授 里希特将考虑导致涉及能力的问题， 解析函数类的例外集。 本研究涉及到Hilbert空间算子理论。 这些算子可以被认为是复数的无限矩阵 号码 它们几乎适用于纯化学的每一个分支， 应用数学 里希特教授的研究对象是 分类和理解一个重要的家庭这样的运营商。

Professor Richter will study the structure of multiplication by z on a generalized Dirichlet space. He will attempt to understand the structure of the invariant subspaces of this operator. When the corresponding measure on the unit disk is Lebesgue measure, then the operator theoretic problems Professor Richter will consider lead to questions involving capacities and exceptional sets of classes of analytic functions. This research involves the theory of Hilbert space operators. These operators can be thought of as infinite matrices of complex numbers. They find application in almost every branch of pure and applied mathematics. The object of Professor Richter's research is to classify and understand an important family of such operators.