The Breadth-one $D$-invariant Polynomial Subspace
This provides a theoretical unification and constructive result for ideal interpolation in the context of D-invariant subspaces, which is incremental for specialists in algebraic interpolation.
The paper proves that two previously defined classes of D-invariant polynomial subspaces are equivalent, both representing breadth-one D-invariant subspaces, and solves the discrete approximation problem for ideal interpolation by finding coalescing points whose evaluation functionals converge to the functional space induced by such a subspace.
We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve the discrete approximation problem in ideal interpolation for the breadth-one $D$-invariant subspace. Namely, we find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given $D$-invariant subspace, as the evaluation points all coalesce at one point.