4867 East Hall
Phone: (734) 764-6419
Most of my research has been related in some way to complex analysis. Broadly speaking, my two main areas of interest are geometric function theory and linear spaces of analytic functions. In geometric function theory I have specialized in variational methods for the solution of extremal problems. The linear spaces have been primarily Hardy spaces (or Hp spaces) and Bergman spaces, where there is often an elegant interplay of complex function theory with functional analysis. Other topics of interest are orthogonal polynomials, hypergeometric functions, and other special functions; potential theory and the notion of Robin capacity; harmonic mappings and their lifts to minimal surfaces; and history of mathematics. For the last ten years I have been investigating Schwarzian derivatives of analytic functions and harmonic mappings as an indicator of geometric properties such as valence and distortion.