Surjective partial differential operators on real analytic functions defined on open convex sets |
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Authors: | M Langenbruch |
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Institution: | (1) University of Oldenburg, Department of Mathematics, 26111 Oldenburg, Germany e-mail: langenbruch@mathematik.uni-oldenburg.de, DE |
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Abstract: | Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on a covex open set Ω⊂ℝ
n
. Let L(P
m
) denote the localizations at ∞ (in the sense of H?rmander) of the principal part P
m
. Then Q(x+iτN)≠ 0 for (x,τ)∈ℝ
n
×(ℝ\{ 0}) for any Q∈L(P
m
) if N is a normal to δΩ which is noncharacteristic for Q. Under additional assumptions this implies that P
m
must be locally hyperbolic.
Received: 24 January 2000 |
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Keywords: | Mathematics Subject Classification (2000): 35E20 35E05 35A18 35A21 |
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