Mathematical Sciences: Operator Theory and Analytic Functions

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This research project examines the invariant subspace structure of multiplication operators on Hilbert spaces of analytic functions. Research will involve multiple pathologies that arise on a space of the mean-square closure of the polynomials with respect to measures on the unit disk; invariant subspaces in Bergman spaces which arise from multiple boundary points; the discovery of metric criterion for the space of polynomial approximants; and the generalization of asymptotic kernel function estimates of T. Trent to general Bergman spaces. This research is in the general mathematical area called 'modern analysis'. Much of modern analysis concerns the study of the spaces of functions or the analytic operators on a specified space. Modern analysis has many applications for physics and geometry.