Displaying similar documents to “Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type”

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 ( ω ) ( Ω ) denote the non-quasianalytic class of Beurling type on an open set Ω in n . For μ ( ω ) ' ( n ) the surjectivity of the convolution operator T μ : ( ω ) ( Ω 1 ) ( 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...

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).

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

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

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G 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.

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.

Standard exact projective resolutions relative to a countable class of Fréchet spaces

P. Domański, J. Krone, D. Vogt (1997)

Studia Mathematica

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We will show that for each sequence of quasinormable Fréchet spaces ( E n ) there is a Köthe space λ such that E x t 1 ( λ ( A ) , λ ( A ) = E x t 1 ( λ ( A ) , E n ) = 0 and there are exact sequences of the form . . . λ ( A ) λ ( A ) λ ( A ) λ ( A ) E n 0 . If, for a fixed ℕ, E n is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form 0 λ ( A ) λ ( A ) E n 0 . The result has some applications in the theory of the functor E x t 1 in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.