Constanze Liaw, Texas A&M University
Unitary rank one perturbations and the adjoint to the Clark operator

Although the Clark operator was introduced over half a century ago, no complete representation formula has been published for its adjoint. However, partial representations have led to important results in Spectral Theory using Harmonic and Complex Analysis, and vice versa. Using vector-valued Functional Models, we derive a complete representation for the adjoint to the Clark operator.