Mathematical Sciences: Analysis on Spaces of Analytic Functions

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The theory of analytic functions of a complex variable (those that are expandable in power series, so roughly speaking the limits of complex polynomials) has enriched all of mathematics for over a century. Such functions enjoy many remarkable properties, for instance that their values at points inside a closed curve are determined completely by their values on the curve. It happens that such functions readily aggregate themselves into Hilbert spaces, and the theory of operators on Hilbert space gains extra vividness when specialized to these spaces of analytic functions. The investigators will study specific classes of operators on the Hardy, Bergman, and Dirichlet function spaces, as well as algebras of bounded analytic functions on the unit disc.