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ISSN 1088-6850(e) ISSN 0002-9947(p)

The geometry of analytic varieties satisfying the local Phragmén-Lindelöf condition and a geometric characterization of the partial differential operators that are surjective on $\mathcal{A}(\mathbb{R} ^4)$

Author(s): Rüdiger W. Braun; Reinhold Meise; B. A. Taylor
Journal: Trans. Amer. Math. Soc. 356 (2004), 1315-1383.
MSC (2000): Primary 32C25; Secondary 32U05, 35E10
Posted: October 21, 2003
MathSciNet review: 2034311
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Abstract: The local Phragmén-Lindelöf condition for analytic subvarieties of $\mathbb{C} ^n$ at real points plays a crucial role in complex analysis and in the theory of constant coefficient partial differential operators, as Hörmander has shown. Here, necessary geometric conditions for this Phragmén-Lindelöf condition are derived. They are shown to be sufficient in the case of curves in arbitrary dimension and of surfaces in $\mathbb{C} ^3$ . The latter result leads to a geometric characterization of those constant coefficient partial differential operators which are surjective on the space of all real analytic functions on $\mathbb{R} ^4$ .

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