Analysis of functions into simpler components, such as complex exponentials, wavelets, etc., and synthesis of operators on function spaces, form two parts of the modern functional analytic approach. Members of our department do research on topics including connections with singular integral operators and PDE, eigenfunction expansions and convergence questions, noncommutative harmonic analysis, operator theory on Hilbert spaces, subnormal and composition operators, operator algebras, operator K-theory, and the ergodic theory of operators.