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.
