On kernels of Toeplitz operators

Abstract

We apply the theory of de Branges–Rovnyak spaces to describe kernels of some Toeplitz operators on the classical Hardy space H^2. In particular, we discuss the kernels of the operators T_{{bar{f}}/ f} and T_{{bar{I}}{bar{f}}/ f}, where f is an outer function in H^2 and I is inner such that I(0)=0. We also obtain a result on the structure of de Branges–Rovnyak spaces generated by nonextreme functions.