exists h and for which there E D'(IR) such that 0+ if and only if ht(xfie) converges to h} in O'(R), a < 0 PROOF. , as a - 0+ . 1. The necessity holds since convergence in Oa(D) implies convergence in D'(IR). A distributional version of the Painleve theorem adapted for our purposes can be formulated and proved as follows.
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