Download Algebraic Approach to Differential Equations by Dung Trang Le PDF

By Dung Trang Le

Blending basic effects and complicated equipment, Algebraic method of Differential Equations goals to accustom differential equation experts to algebraic equipment during this niche. It provides fabric from a faculty equipped by way of The Abdus Salam overseas Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the foreign Centre for natural and utilized arithmetic (CIMPA).

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6 in,2 and gives a very precise information about the spaces of solutions E(I) and F (I). 5. Let I ⊂ D be a non-zero left ideal and Fp , . . , Fq a Gr¨ obner basis of I. Then the following properties hold: (1) (2) (3) (4) E(I) = ker(Fp : A → A)(= E(DFp )). F (I) = ker(Fq : M → M)(= E(DFq )). dimC E(I) = p(I)(= p = ord(Fp )), dimC F (I) = ν(I)(= ν(Fq )). P ∈ I ⇔ P f = 0, ∀f ∈ E(I) and P g = 0, ∀g ∈ F (I). Proof. 3, (1) and the fact that A has no O-torsion. For property (2), we only need to prove that any g ∈ M annihilated by Fq is annihilated by Fp , .

The above results are the precursors of the irregularity complexes along a hypersurface and the notion of regular holonomic module in higher dimension (see the papers20,21 ). 29 11. A Local Version of the Riemann-Hilbert Correspondence in One Variable (in Collaboration with F. 5 in13 using the description of simple objects in the category C instead of the more involved description of indecomposable objects (see the master thesis7 ). 1. Let us call C0 the category defined in the following way: (1) The objets of C0 are the diagrams (E, F, u, v) where E, F are complex vector spaces and u : E → F and v : F → E are linear maps such that IdE + v ◦ u and IdF + u ◦ v are automorphisms.

1981. 5. E. Goursat. Cours d’analyse math´ematique, Tome II. Gauthier-Villars, Paris, 1933. 6. M. Granger and Ph. Maisonobe. A basic course on differential modules, in16 vol. I, 103–168. 7. F. Gudiel Rodr´ıguez. Sobre una variante local del problema de RiemannHilbert en una variable. Tesis de Licenciatura, Facultad de Matem´ aticas, Universidad de Sevilla, October 1991. 8. O. Ince. Ordinary Differential Equations. Dover, New York, 1950. 9. B. Iversen. Cohomology of Sheaves. Universitext. Springer Verlag, Heidelberg, 1986.

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