Gevrey vectors of multi-quasi-elliptic differential operators
by
Chikh Bouzar
Department of Mathematics. Oran-Essenia University. Algeria
Coauthors: Rachid Chaili

We give definitions of the space of Gevrey vectors of the system ( P_j( x, D) ) _j=1^L, noted G^s( \Omega, ( P_j) _j=1^L) , and the space of Gevrey classes with respect to the Newton's polyhedron \digamma associated to the system ( P_j( x, D) ) _j=1^L, noted G_\digamma ^s(\Omega), and after we prove a theorem resolving the folowing problem : Find algebraic necessary and sufficient conditions such that the next inclusion holds G^s( \Omega, ( P_j) _j=1^L) subset G_\digamma ^s(\Omega). The result obtained generalise the theorems of Komatsu, Kotake-Narasimhan and others...

Date received: August 11, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahz-99.