Let $P$ be a linear partial differential operator with coefficients in the Gevrey class $G^s(T^n)$ where $T^n$ is the $n$-dimensional torus and $s\geq 1$. We prove that if $P$ is $s$-globally hypoelliptic in $T^n$ then its transpose operator $^tP$ is $s$-globally solvable in $T^n$, thus extending to the Gevrey classes the well-known analogous result of HORMANDER in the corresponding $C^\infty$ class.
Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus
ALBANESE, Angela Anna;
2004-01-01
Abstract
Let $P$ be a linear partial differential operator with coefficients in the Gevrey class $G^s(T^n)$ where $T^n$ is the $n$-dimensional torus and $s\geq 1$. We prove that if $P$ is $s$-globally hypoelliptic in $T^n$ then its transpose operator $^tP$ is $s$-globally solvable in $T^n$, thus extending to the Gevrey classes the well-known analogous result of HORMANDER in the corresponding $C^\infty$ class.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
