Kernels of Toeplitz Operators and Rational Interpolation

The kernel of a Toeplitz operator on the Hardy class H 2 in the unit disk is a nearly invariantsubspace of the backward shift operator, and, by D. Hitt’s result, it has the form g · K ω where ω is an inner function, K ω = H 2 ⊝ ωH 2 , and g is an isometric multiplier on K ω . We describe the functions ω and g for the kernel of the Toeplitz operator with symbol . θ ¯ Δ where θ is an inner function and Δ is a finite Blaschke product.