Picard--Vessiot extensions for linear functional systems

Picard-Vessiot extensions for ordinary differential and difference equations are well known and are at the core of the associated Galois theories. In this paper, we construct fundamental matrices and Picard-Vessiot extensions for systems of linear partial functional equations having finite linear dimension. We then use those extensions to show that all the solutions of a factor of such a system can be completed to solutions of the original system. Categories and Subject Descriptors

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: Manuel Bronstein, Ziming Li, Min Wu
• Keywords: Associated Galois Theories, ISSAC 2005, Partial Functional Equations, Picard-Vessiot Extensions