Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type
Let denote the space of all ω-ultradifferentiable functions of Roumieu type on an open interval I in ℝ. In the special case ω(t) = t we get the real-analytic functions on I. For with one can define the convolution operator , . We give a characterization of the surjectivity of for quasianalytic classes , where I = ℝ or I is an open, bounded interval in ℝ. This characterization is given in terms of the distribution of zeros of the Fourier Laplace transform of μ.