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We show that for a partial differential operator P (D) surjectivity on the space of ultradistributions D ′ (ω)(Ω) of Beurling type is equivalent to surjectivity of P (D) on C∞(Ω) in case of Ω being an open subset of R.

Surjectivity of partial differential operators on ultradistributions of Beurling type in two dimensions