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 · Kω where ω is an inner function, Kω = H2 ⊝ ωH2, and g is an isometric multiplier on Kω. 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.