An extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebra - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

An extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebra

Yves Colin de Verdière

Résumé

Motivated by many recent works (by L. Charles, V. Guillemin, T. Paul, J. Sjöstrand, A. Uribe, S. Vu Ngoc, S. Zelditch and others) on the semi-classical Birkhoff normal forms, we investigate the structure of the group of automorphisms of the graded semi-classical Weyl algebra which is used to get the normal forms. The answer is quite similar to the Theorem of Duistermaat and Singer for the usual algebra of pseudo-differential operators where all automorphisms are given by conjugation by an elliptic Fourier Integral Operator (a FIO). Here what replaces general non-linear symplectic diffeomeorhisms is just linear complex symplectic maps, because everything is localized at a single point.
Fichier principal
Vignette du fichier
autom.pdf (98.97 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00362384 , version 1 (18-02-2009)

Identifiants

Citer

Yves Colin de Verdière. An extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebra. 2009. ⟨hal-00362384⟩
54 Consultations
57 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More