On a functional index of hypoellipticity

The concept of hypoellipticity weight, which generalizes Hörmander's concept of index of hypoellipticity, is introduced for linear differential operators with constant coefficients. Exact formulas are derived for the hypoellipticity weight of regular hypoelliptic operators. These formulas are applied to determine more exactly the Gevrey classes to which the solutions of a regular hypoelliptic equation belong. The results are shown to be unimprovable in terms of Gevrey classes.
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