Let P be a linear partial differential operator with coefficients in the Gevrey class Gs. We prove first that if P is s–hypoelliptic then its transposed operator tP is s–locally solvable, thus extending to the Gevrey classes the well–known analogous result in the C∞ class. We prove also that if P is s–hypoelliptic then its null space is finite dimensional and its range is closed; this implies an index theorem for s–hypoelliptic operators. Generalizations of these results to other classes of functions are also considered.

Hypoellipticity and local solvability in Gevrey classes

CORLI, Andrea;
2002

Abstract

Let P be a linear partial differential operator with coefficients in the Gevrey class Gs. We prove first that if P is s–hypoelliptic then its transposed operator tP is s–locally solvable, thus extending to the Gevrey classes the well–known analogous result in the C∞ class. We prove also that if P is s–hypoelliptic then its null space is finite dimensional and its range is closed; this implies an index theorem for s–hypoelliptic operators. Generalizations of these results to other classes of functions are also considered.
2002
Albanese, A. A.; Corli, Andrea; Rodino, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1199918
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