Nearly Invariant Subspaces and Rational Interpolation

Given an inner function θ in the upper half-plane, consider the subspace H 2 ⊖ θH 2 of the Hardy space H 2 . For a finite collection Λ of points on the complex plane, the subspace of functions from K θ that vanish on Λ can be represented in the form g ∙ K ω , where ω is an inner function and g is an isometric multiplier on K ω . We obtain a description of the functions ω and g in terms of θ and Λ.