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Sur les fonctions C et les distributions qui appartiennent à la classe de Bernstein

Jean-Claude Tougeron (1979)

Annales de l'institut Fourier

Soient 𝔑 n (resp. n ) l’anneau des germes de fonctions de Nash (resp. l’anneau des germes de fonctions C ) à l’origine de R n : n (resp. n ' ) le module sur 𝔑 n des germes de fonctions de Bernstein C (resp. le module sur 𝔑 n des germes de distributions de Bernstein) à l’origine de R n . Les deux résultats principaux de l’article sont les suivants : n ' est un module injectif sur 𝔑 n et n / n est un module plat sur 𝔑 n .

Surjective convolution operators on spaces of distributions.

Leonhard Frerick, Jochen Wengenroth (2003)

RACSAM

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.

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

Thomas Meyer (1997)

Studia Mathematica

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.

Systems of convolution equations and LAU-spaces

Daniele C. Struppa (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Dato un sistema omogeneo di equazioni di convoluzione in spazi dotati di strutture analiticamente uniformi, si forniscono condizioni per ottenere teoremi di rappresentazione per le sue soluzioni.

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