Topics in Function Theoretic Operator Theory

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Professor Conway will investigate several topics in the theory of subnormal operators and in several variable operator theory. Some of these questions are related to the recent breakthrough of J.E. Thomson showing that bounded point evaluations exist in interesting cases. Another question involves finding a functional calculus for subnormal n-tuples of operators. This research involves the theory of Hilbert space operators. These operators are essentially infinite matrices of complex numbers. Such objects have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important classes of these operators.