The structure of a second-degree DD-invariant subspace and its application in ideal interpolation

The DD-invariant polynomial subspaces play a crucial role in ideal interpolation. In this paper, we analyze the structure of a second-degree DD-invariant polynomial subspace P2P2. As an application for ideal interpolation, we solve the discrete approximation problem for δzP2(D) under certain conditions, i.e., we compute pairwise distinct points, such that the limiting space of the evaluation functionals at these points is the given space δzP2(D), as the evaluation sites all coalesce at one site z.