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Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set $Ω \subset ℝ^{n}$ . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization $P_{m, Θ}$ of the principal part $P_{m}$ is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for $P_{m, Θ}$ . Under additional assumptions $P_{m}$ must be locally hyperbolic.

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