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The structure of a second-degree \(D\)-invariant subspace and its application in ideal interpolation. (English) Zbl 1382.41002

Summary: The \(D\)-invariant polynomial subspaces play a crucial role in ideal interpolation. In this paper, we analyze the structure of a second-degree \(D\)-invariant polynomial subspace \(P_2\). As an application for ideal interpolation, we solve the discrete approximation problem for \(\delta_{\mathbf{z}} P_2(D)\) 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 \(\delta_{\mathbf{z}} P_2(D)\), as the evaluation sites all coalesce at one site \(\mathbf{z}\).

MSC:

41A05 Interpolation in approximation theory
13N15 Derivations and commutative rings
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