Local solvability of linear differential operators with double characteristics I: Necessary conditions
Detlef Mueller
Abstract
This is a the first in a series of two articles devoted to the question of local solvability of doubly characteristic differential operators L, defined, say, in an open set ⊂ n. Suppose the principal symbol pk of L vanishes to second order at (x0,ξ0)∈ T* 0, and denote by Q the Hessian form associated to pk on T(x0,ξ0)T*. As the main result of this paper, we show (under some rank conditions and some mild additional conditions) that a necessary condition for local solvability of L at x0 is the existence of some θ∈ such that (eiθQ) 0.
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