Continuous division of differential operators

Herwig Hauser[1]; Luis Narváez-Macarro[2]

  • [1] Universität Innsbruck, Mathematisches Institut, 6020 Innsbruck (Autriche)
  • [2] Universidad de Sevilla, Facultad de Matematicas, Departamento de Algebra, 4101 Sevilla (Espagne)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 3, page 769-778
  • ISSN: 0373-0956

Abstract

top
In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.

How to cite

top

Hauser, Herwig, and Narváez-Macarro, Luis. "Continuous division of differential operators." Annales de l’institut Fourier 51.3 (2001): 769-778. <http://eudml.org/doc/115929>.

@article{Hauser2001,
abstract = {In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.},
affiliation = {Universität Innsbruck, Mathematisches Institut, 6020 Innsbruck (Autriche); Universidad de Sevilla, Facultad de Matematicas, Departamento de Algebra, 4101 Sevilla (Espagne)},
author = {Hauser, Herwig, Narváez-Macarro, Luis},
journal = {Annales de l’institut Fourier},
keywords = {differential operators; division theorems; continuity},
language = {eng},
number = {3},
pages = {769-778},
publisher = {Association des Annales de l'Institut Fourier},
title = {Continuous division of differential operators},
url = {http://eudml.org/doc/115929},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Hauser, Herwig
AU - Narváez-Macarro, Luis
TI - Continuous division of differential operators
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 3
SP - 769
EP - 778
AB - In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.
LA - eng
KW - differential operators; division theorems; continuity
UR - http://eudml.org/doc/115929
ER -

References

top
  1. J. Briançon, P. Maisonobe, Idéaux de germes d'opérateurs différentiels à une variable, Enseign. Math. (2) 30 (1984), 7-38 Zbl0542.14008MR743668
  2. F. Castro, Calcul de la dimension et des multiplicités d’un D -module monogène, C. R. Acad. Sci. Paris, Sér. I Math. 302 (1986), 487-490 Zbl0606.32007MR844148
  3. H. Hauser, Singular differential equations Zbl0631.32005
  4. H. Hauser, M. Müller, A Rank Theorem for analytic maps between power series spaces, Inst. Hautes Études Sci. Publ. Math. 80 (1994), 95-115 Zbl0831.58008MR1320605
  5. H. Hauser, J.-J. Risler, B. Teissier, The reduced Bautin index of planar vector fields, Duke Math. J. 100 (1999), 425-445 Zbl0947.34013MR1719738
  6. Z. Mebkhout, L. Narváez-Macarro, Le théorème de continuité de la division dans les anneaux d'opérateurs différentiels, J. reine angew. Math. 503 (1998), 193-236 Zbl0910.32011MR1650272

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.