2012
DOI: 10.1016/j.crma.2012.03.006
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Constrained extensions of real type

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Cited by 5 publications
(6 citation statements)
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“…K ⊂ E ⊂ L, then L|E is a real Picard-Vessiot extension and DGal(L|E) is a C-defined closed subgroup of DGal(L|K). As in the ordinary case (see [5] Theorem 3.1, [6] Theorem 4.4), we obtain a Galois correspondence theorem. Theorem 4.…”
Section: Galois Correspondencementioning
confidence: 55%
See 2 more Smart Citations
“…K ⊂ E ⊂ L, then L|E is a real Picard-Vessiot extension and DGal(L|E) is a C-defined closed subgroup of DGal(L|K). As in the ordinary case (see [5] Theorem 3.1, [6] Theorem 4.4), we obtain a Galois correspondence theorem. Theorem 4.…”
Section: Galois Correspondencementioning
confidence: 55%
“…, u m . Now, by [5] Corollary 2.6, there exists a real field F which is a Picard-Vessiot extension of K D for (2). Clearly F (i) is a Picard-Vessiot extension of K D (i) for (2).…”
Section: Existence Of Real Picard-vessiot Extensionsmentioning
confidence: 99%
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“…In [4] and [5], we proved the existence of a Picard-Vessiot extension for linear differential equations defined over a real differential field with a real closed field of constants C, we gave an appropriate definition of its differential Galois group, proved that it has the structure of a C-defined linear algebraic group and established a Galois correspondence theorem in this setting. In [6], Gel'fond and Khovanskii characterized Liouville functions over R using differential rings of real functions with a finiteness property.…”
Section: Introductionmentioning
confidence: 99%
“…A real Picard-Vessiot field L for M/K is a Picard-Vessiot field which is also a real field. In [CHS1] and [CHS2] the existence of a real Picard-Vessiot field is proved using results of Kolchin.…”
Section: Introductionmentioning
confidence: 99%