Displaying similar documents to “On the range of convolution operators on non-quasianalytic ultradifferentiable functions”

Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type

Thomas Meyer (1997)

Studia Mathematica

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Let ε ω ( I ) 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 μ ∈ ε ω ( I ) ' with s u p p ( μ ) = 0 one can define the convolution operator T μ : ε ω ( I ) → ε ω ( I ) , T μ ( f ) ( x ) : = ⟨ μ , f ( x - · ) ⟩ . We give a characterization of the surjectivity of T μ for quasianalytic classes ε ω ( I ) , 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 μ ^ of μ.

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.

Continuous linear right inverses for convolution operators in spaces of real analytic functions

Michael Langenbruch (1994)

Studia Mathematica

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We determine the convolution operators T μ : = μ * on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).

Surjective convolution operators on spaces of distributions.

Leonhard Frerick, Jochen Wengenroth (2003)

RACSAM

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We review recent developments in the theory of inductive limits and use them to give a new and rather easy proof for Hörmander?s characterization of surjective convolution operators on spaces of Schwartz distributions.

Some remarks on convolution equations

C. A. Berenstein, M. A. Dostal (1973)

Annales de l'institut Fourier

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Using a description of the topology of the spaces E ' ( Ω ) ( Ω open convex subset of R n ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution T , T ∈ E ' . We give applications to a class of distributions T satisfying cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T for all S ∈ E ' .