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Serre's reduction of linear partial differential systems with holonomic adjoints

Thomas Cluzeau 1 Alban Quadrat 2, 3
1 DMI
XLIM - XLIM
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : Given a linear functional system (e.g., ordinary/partial differential systems, differential time-delay systems, difference systems), Serre's reduction aims at finding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre's reduction of underdetermined linear systems of partial differential equations with either polynomial, formal power series or analytic coefficients and with holonomic adjoints in the sense of algebraic analysis. We prove that these linear partial differential systems can be defined by means of a single linear partial differential equation. In the case of polynomial coefficients, we give an algorithm to compute the corresponding equation.
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Submitted on : Tuesday, December 14, 2010 - 5:55:39 PM
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Thomas Cluzeau, Alban Quadrat. Serre's reduction of linear partial differential systems with holonomic adjoints. [Research Report] RR-7486, INRIA. 2010, pp.36. ⟨inria-00545658v2⟩

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