Liouvillian solutions of linear difference–differential equations

For a field k with an automorphism σ and a derivation δ , we introduce the notion of Liouvillian solutions of linear difference–differential systems { σ ( Y ) = A Y , δ ( Y ) = B Y } over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the fo...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 45; no. 3; pp. 287 - 305
Main Authors Feng, Ruyong, Singer, Michael F., Wu, Min
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2010
Subjects
Galois theory
Linear difference–differential equations
Liouvillian sequences
Liouvillian sequences
Linear difference–differential equations
Galois theory
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Summary:For a field k with an automorphism σ and a derivation δ , we introduce the notion of Liouvillian solutions of linear difference–differential systems { σ ( Y ) = A Y , δ ( Y ) = B Y } over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear difference–differential systems of prime order have Liouvillian solutions.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2009.09.001