Differential systems of pure Gaussian type
Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 189-220.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give the transformation rule for the Stokes data of the Laplace transform of a differential system of pure Gaussian type.
Keywords: meromorphic connection, Stokes matrix.
Mots-clés : Laplace transformation
@article{IM2_2016_80_1_a6,
     author = {C. Sabbah},
     title = {Differential systems of pure {Gaussian} type},
     journal = {Izvestiya. Mathematics },
     pages = {189--220},
     publisher = {mathdoc},
     volume = {80},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a6/}
}
TY  - JOUR
AU  - C. Sabbah
TI  - Differential systems of pure Gaussian type
JO  - Izvestiya. Mathematics 
PY  - 2016
SP  - 189
EP  - 220
VL  - 80
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a6/
LA  - en
ID  - IM2_2016_80_1_a6
ER  - 
%0 Journal Article
%A C. Sabbah
%T Differential systems of pure Gaussian type
%J Izvestiya. Mathematics 
%D 2016
%P 189-220
%V 80
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a6/
%G en
%F IM2_2016_80_1_a6
C. Sabbah. Differential systems of pure Gaussian type. Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 189-220. http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a6/

[1] P. Deligne, “Lettre à B. Malgrange du 19/4/1978”, Singularités irrégulières, Correspondance et documents, Doc. Math. (Paris), 5, Soc. Math. France, Paris, 2007, 25–26 | MR | Zbl

[2] B. Malgrange, Équations différentielles à coefficients polynomiaux, Progr. Math., 96, Birkhäuser Boston, Inc., Boston, MA, 1991, vi+232 pp. | MR | Zbl

[3] A. D'Agnolo, M. Kashiwara, Riemann–Hilbert correspondence for holonomic $D$-modules, 2013, arXiv: 1311.2374

[4] M. Hien, C. Sabbah, “The local Laplace transform of an elementary irregular meromorphic connection”, Rend. Semin. Mat. Univ. Padova, 134 (2015), 133–196 ; (2014), arXiv: 1405.5310 | DOI | MR | Zbl

[5] T. Mochizuki, Holonomic $\mathcal D$-modules with Betti structure, Mém. Soc. Math. Fr. (N. S.), 138–139, Soc. Math. France, Paris, 2014, viii+205 pp. | Zbl

[6] T. Mochizuki, “Note on the Stokes structure of the Fourier transform”, Acta Math. Vietnam., 35:1 (2010), 107–158 | MR | Zbl

[7] C. Sabbah, Introduction to Stokes structures, Lecture Notes in Math., 2060, Springer, Heidelberg, 2013, xiv+249 pp. | DOI | MR | Zbl

[8] D. Arinkin, “Rigid irregular connections on $\mathbb{P}^1$”, Compos. Math., 146:5 (2010), 1323–1338 | DOI | MR | Zbl

[9] C. Sabbah, “An explicit stationary phase formula for the local formal Fourier–Laplace transform”, Singularities, v. 1, Contemp. Math., 474, Amer. Math. Soc., Providence, RI, 2008, 309–330 | DOI | MR | Zbl

[10] C. Sabbah, “Monodromy at infinity and Fourier transform. II”, Publ. Res. Inst. Math. Sci., 42:3 (2006), 803–835 | DOI | MR | Zbl

[11] B. Malgrange, “La classification des connexions irrégulières à une variable”, Mathematics and physics (Paris, 1979/1982), Progr. Math., 37, Birkhäuser Boston, Boston, MA, 1983, 381–399 | MR | Zbl

[12] D. G. Babbitt, V. S. Varadarajan, Local moduli for meromorphic differential equations, Astérisque, 169–170, Soc. Math. France, Paris, 1989, 217 pp. | MR | Zbl

[13] C. Hertling, C. Sabbah, “Examples of non-commutative Hodge structure”, J. Inst. Math. Jussieu, 10:3 (2011), 635–674 | DOI | MR | Zbl

[14] R. Godement, Topologie algébrique et théorie des faisceaux, Publ. Inst. Math. Univ. Strasbourg, XIII, Actualités Sci. Indust., No 1252, Hermann, Paris, 1958, viii+283 pp. | MR | Zbl | Zbl

[15] C. Sabbah, Isomonodromic deformations and Frobenius manifolds. An introduction, transl. from the 2002 French ed., Universitext, Springer-Verlag London, Ltd., London; EDP Sciences, Les Ulis, 2007, xiv+279 pp. | MR | Zbl

[16] C. Sabbah, Équations différentielles à points singuliers irréguliers et phénomène de Stokes en dimension 2, Astérisque, 263, Soc. Math. France, Paris, 2000, viii+190 pp. | MR | Zbl

[17] C. Sabbah, “Équations différentielles à points singuliers irréguliers en dimension $2$”, Ann. Inst. Fourier (Grenoble), 43:5 (1993), 1619–1688 | DOI | MR | Zbl

[18] H. Majima, Asymptotic analysis for integrable connections with irregular singular points, Lecture Notes in Math., 1075, Springer-Verlag, Berlin, 1984, x+159 pp. | DOI | MR | Zbl