A characterization of the Khavinson-Shapiro conjecture via Fischer operators

The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that property (KS) for a domain $Ω$ is equivalent to the surjectivity of a Fischer operator associated to the domain $Ω.$

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