Abstract
In our recently published paper “On the closure of translation–dilation invariant linear spaces of polynomials” (see original article), there was an error. Namely, the decomposition of ΩV given after Lemma 8 in original article does not hold for d 3 for some TDI-subspaces of R[x]. For example, the TDIsubspace V = span{x1x2x3 : a 1, b 2} of R[x1, x2, x3] does not possess such a decomposition. This fact was pointed to the authors by Prof. Georg Zimmermann after publication of the paper. Below we give a new proof of the main result of original article avoiding such a hypothesis. We use the notation introduced in original article.
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