In this paper we extend a well-known result concerning hypoellipticity and local solvability of linear partial differential operators on Schwartz distributions to the framework of pseudolocal continuous linear maps T acting on Gevrey classes. Namely we prove that the Gevrey hypoellipticity of T implies the Gevrey local solvability of the transposed operator. As an application, we identify some classes of non-Gevrey-hypoelliptic operators. A fundamental kernel is also constructed for any Gevrey hypoelliptic partial differential operator.

Hypoellipticity and local solvability of pseudolocal continuous linear operators in Gevrey classes

MORANDO, Alessandro
2004-01-01

Abstract

In this paper we extend a well-known result concerning hypoellipticity and local solvability of linear partial differential operators on Schwartz distributions to the framework of pseudolocal continuous linear maps T acting on Gevrey classes. Namely we prove that the Gevrey hypoellipticity of T implies the Gevrey local solvability of the transposed operator. As an application, we identify some classes of non-Gevrey-hypoelliptic operators. A fundamental kernel is also constructed for any Gevrey hypoelliptic partial differential operator.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/147
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