Remarks on the Levi conditions for differential systems (Q949097)

In \textit{J. Vaillant} [C. R. Acad. Sc. Paris, Sér. I 313, No. 5, 227--230 (1991; Zbl 0755.35064)] a general definition of Levi conditions was given for weakly hyperbolic systems of linear operators with analytic coefficients, under the assumption of constant multiplicity of the characteristics. Here the authors discuss in detail such conditions, proving in particular that in the scalar case they are equivalent to the usual Gevrey-Levi conditions. A second interesting application concerns systems where the principal symbol has a Jordan form made of a large number of \(2\times 2\) blocks.