The formal classification of linear difference operators

Praagman, C.

doi:10.1016/1385-7258(83)90061-6

Cited by 30 publications

(24 citation statements)

References 2 publications

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“…This is, an immediate consequence of the properties of the Newton polygon studied in [28], [29], [32]. For a more explicit analytic proof see [7] (see also [19]). ✷…”

Section: The Category E F Of Fuchsian Equationsmentioning

confidence: 94%

Galois theory of fuchsian q-difference equations

Sauloy¹

2003

Annales Scientifiques de l’École Normale Supérieure

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RésuméNous proposons une approche analytique de la théorie de Galois des systèmes aux q-différences linéaires singuliers réguliers. Nous combinons la dualité de Tannaka avec la méthode de classification de Birkhoffà l'aide de la matrice de connexion pour définir et décrire leurs groupes de Galois. Puis nous décrivons des sous-groupes fondamentaux qui donnent lieuà une correspondance de Riemann-Hilbert età un théorème de densité de type Schlesinger. AbstractWe propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups. Then we describe fundamental subgroups that give rise to a Riemann-Hilbert correspondence and to a density theorem of Schlesinger's type.

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“…This is, an immediate consequence of the properties of the Newton polygon studied in [28], [29], [32]. For a more explicit analytic proof see [7] (see also [19]). ✷…”

Section: The Category E F Of Fuchsian Equationsmentioning

confidence: 94%

Galois theory of fuchsian q-difference equations

Sauloy¹

2003

Annales Scientifiques de l’École Normale Supérieure

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“…[17,8]). If the convergent series A c is identified with its sum, the canonical operator ∆ c can be viewed as an analytic difference operator, and the homogeneous equation ∆ c y = 0 has a fundamental system of analytic solutions {y j : j = 1, .…”

Section: Levels and Stokes Directionsmentioning

confidence: 99%

Accelero-summation of the formal solutions of nonlinear difference equations

Immink¹

2011

Ann. inst. Fourier

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“…Since Turrittin [8], the formal reduction of difference systems or of difference equations has been studied in many ways [4], [5], [7]. The different methods lead to the result of Turrittin either in forms of classification or in forms of formal solutions.…”

Section: Introduction and Notationsmentioning

confidence: 99%