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

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

Studia Mathematica

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 μ ω ' ( n ) . These...

Opérateurs pseudo-différentiels définis en un point

Ryuichi Ishimura (2006)

Annales Polonici Mathematici

We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi, Mariel Saez (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

Syzygies of modules and applications to propagation of regularity phenomena.

Alex Meril, Daniele C. Struppa (1990)

Publicacions Matemàtiques

Propagation of regularity is considered for solutions of rectangular systems of infinite order partial differential equations (resp. convolution equations) in spaces of hyperfunctions (resp. C∞ functions and distributions). Known resulys of this kind are recovered as particular cases, when finite order partial differential equations are considered.

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