Professors Olin and Thomson will continue their work on subnormal operator theory and its associated function theory problems. This includes the study of various algebras generated by the subnormal operators and their associated representations. The study of the function spaces associated to these algebras will also be pursued. This work may have applications to several areas of mathematics including measure theory, Borel analysis, ergodic theory, and function theory. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to categorize certain important classes of such objects.
