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

• Autorzy: Jóse Bonet , Antonio Galbis , R. Meise
• Języki publikacji: EN

Abstrakty

EN

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 $μ ∈ ℇ'_{{ω}}(ℝ^n)$. These results extend classical work of Hörmander on convolution operators between spaces of $C^∞$-functions and more recent one of Ciorănescu and Braun, Meise and Vogt.

Kategorie tematyczne

• 35R50: Partial differential equations of infinite order
• 45F05: Systems of nonsingular linear integral equations
• 46F10: Operations with distributions
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 126
• Numer: 2
• Strony: 171-198

Daty

wydano

1997

otrzymano

1997-02-06

poprawiono

1997-05-19

Twórcy

autor

Jóse Bonet

• Dpto. Matemática Aplicada, Universidad Politécnica, E-46071 Valencia, Spain

autor

Antonio Galbis

• Dpto. Análisis Matemático, Universidad de Valencia, E-46100 Burjasot (Valencia), Spain

autor

R. Meise

• Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Fed. Rep. of Germany

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