Real Liouville Extensions

Abstract

We characterize linear differential equations defined over a real differential field with a real closed field of constants C, which are solvable by real Liouville functions, as those having a differential Galois group whose identity component is solvable and C-split.

Key Words:

• Liouville extension
• Real Picard-Vessiot theory
• Split solvable algebraic group

2010 Mathematics Subject Classification:

• Primary: 12H05
• Secondary: 12D15
• 14P05
• 13B05

Notes

Communicated by A. Elduque.