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Article Dans Une Revue Journal of Differential Equations Année : 2015

q-DEFORMATION OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS

Résumé

In this paper, we consider the behaviour, when q goes to 1, of the set of a convenient basis of meromorphic solutions of a family of linear q-difference equations. In particular, we show that, under convenient assumptions, such basis of meromorphic solutions converges, when q goes to 1, to a basis of meromorphic solutions of a linear differential equation. We also explain that given a linear differential equation of order at least two, which has a Newton polygon that has only slopes of multiplicities one, and a basis of meromorphic solutions, we may build a family of linear q-difference equations that discretizes the linear differential equation, such that a convenient family of basis of meromorphic solutions is a q-deformation of the given basis of meromorphic solutions of the linear differential equation.
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Dates et versions

hal-01897306 , version 1 (17-10-2018)

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Thomas Dreyfus. q-DEFORMATION OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS. Journal of Differential Equations, 2015, 259 (11), pp.5734 - 5768. ⟨10.1016/j.jde.2015.07.010⟩. ⟨hal-01897306⟩
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