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We show a strong factorization theorem of Dixmier–Malliavin type for ultradifferentiable vectors associated with compact Lie group representations on sequentially complete locally convex Hausdorff spaces. In particular, this solves a conjecture by Gimperlein  et al.  [16] for analytic vectors in the case of compact Lie groups.

Strong Factorization of Ultradifferentiable Vectors Associated With Compact Lie Group Representations