Displaying similar documents to “Surjective convolution operators on spaces of distributions.”

On the range of convolution operators on non-quasianalytic ultradifferentiable functions

Jóse Bonet, Antonio Galbis, R. Meise (1997)

Studia Mathematica

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Let ℇ ( ω ) ( Ω ) denote the non-quasianalytic class of Beurling type on an open set Ω in ℝ n . For μ ∈ ℇ ( ω ) ' ( ℝ n ) the surjectivity of the convolution operator T μ : ℇ ( ω ) ( Ω 1 ) → ℇ ( ω ) ( Ω 2 ) is characterized by various conditions, e.g. in terms of a convexity property of the pair ( Ω 1 , Ω 2 ) and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator S μ : D ω ' ( Ω 1 ) → D ω ' ( Ω 2 ) between ultradistributions of Roumieu type whenever...

Solution operators for convolution equations on the germs of analytic functions on compact convex sets in ℂ N

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

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G ⊂ ℂ N is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.