Kernels of Toeplitz Operators and Rational Interpolation

Abstract

The kernel of a Toeplitz operator on the Hardy class H² 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 = H² ⊝ ωH², 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 .\( \overline{\theta}\varDelta \) where θ is an inner function and Δ is a finite Blaschke product.