Classe d'equivalence Formelle D'un D-Module D'Airy

Details Classe d'equivalence Formelle D'un D-Module D'Airy Classe d'equivalence Formelle D'un D-Module D'Airy

2003-06-10

arxiv.org/abs/math/0306170v1

Mathematics

Classical Analysis and ODEs

20 pages, in French

Scientific paper

In this work we study a formal equivalent class of an Airy's D-module, which we compare with an analytic class of equivalence. We calculate the determining factors of an Airy operator of bidegree (n, m) and we clarify the coefficients of the operator which intervene in the determination of the determining factors. Finally, we induce, the canonical model (see [ BV1]), of an Airy operator of bidegre (n, m). ----- Dans ce travail on \'etudie une classe d'\'equivalence formelle d'un D-module d'Airy, qu'on compare avec une classe d'\'equivalence analytique. On calcule les facteurs d\'eterminants d'un op\'erateur d'Airy de bidegr\'e (n,m) et on pr\'ecise les coefficients de l'op\'erateur qui interviennent dans la d\'etermination des facteurs d\'eterminants. On donne enfin, le mod\`ele canonique, voir [BV1], d'un op\'erateur d'Airy de bidegr\'e (n,m).

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