What do real ideal projectors interpolate? Original Research Article

A characterization of interpolation properties of ideal projectors on the space of complex polynomials in several variables was given in [H.M. Möller, Hermite interpolation in several variables using ideal-theoretic methods, in: W. Schempp, K. Zeller (Eds.), Constructive Theory of Functions of Several Variables, in: Lecture Notes in Mathematics, Springer, 1977, pp. 155–163] (cf. also [C. de Boor, A. Ron, On polynomial ideals of finite codimension with applications to box spline theory, J. Math. Anal. Appl. 158 (1991) 168–193]). The purpose of this article is to provide a similar characterization for ideal projectors on the space of real polynomials. Equivalently, we give a description of finite-dimensional DD-invariant subspaces of the space R[[x1,…,xd]]R[[x1,…,xd]] of formal power series in dd indeterminants with real coefficients.