Abstract
The technique of quasi-symmetrizer has been applied to the well-po- sedness of the Cauchy problem for scalar operators (10), (13) and linear sys- tems (5), (15), (4), and to the propagation of analitycity for solutions to semi-linear systems (6). In all these works, it is assumed that the principal symbol depends only on the time variable. In this note we illustrate, in some special cases, a new property of the quasi- symmetrizer which allows us to generalize the result in (6) to semi-linear systems with coefficients depending also on the space variables (21). Such a property is closely connected with some interesting inequalities on the eigenvalues of a hy- perbolic matrix. We expect that this technique applies also to other problems.
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