Picard-Vessiot extensions for real fields

Sowa, Elżbieta

doi:10.1090/S0002-9939-2010-10700-1

Picard-Vessiot extensions for real fields
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Proc. Amer. Math. Soc. 139 (2011), 2407-2413 Request permission

Abstract:

We define a notion of Picard-Vessiot extension for a homogeneous linear differential equation $\mathcal {L}=0$ defined over a real differential field $K$ with a real closed field of constants $C_{K}$. When $\mathcal {L}$ has differential Galois group $GL_{n}$ over the complexification of $K$, we prove that a Picard-Vessiot extension for $\mathcal {L}$ exists over $K$.

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