Differential operators of the first order with degenerate principal symbols

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Title

Authors ¹

Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt, Ostenstr. 28, D-8078 Eichstätt, Germany

Let there be given a differential operator on

ℝ^{n}

of the form

D = \sum^{n}_{i, j = 1} a_{i j} \cdot x_{j} \frac{\partial}{\partial} x_{i} + μ

, where

A = (a_{i j})

is a real matrix and μ is a complex number. We study the following question: To what extent the mapping

D : S' (ℝ^{n}) \to S' (ℝ^{n})

is surjective? We shall give some conditions on A and μ which assure the surjectivity of D.

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