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

Simple item page
dc.creatorDe Verdière, Yves Colin
dc.date2009-02-18
dc.date.accessioned2026-07-07T12:43:30Z
dc.date.available2026-07-07T12:43:30Z
dc.descriptionMotivated 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.
dc.identifierhttps://arxiv.org/abs/0902.3084
dc.identifierhttp://arxiv.org/abs/0902.3084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220442
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject35S30, 53D22, 53D55
dc.titleAn extension of the Duistermaat-Singer Theorem to the semi-classical Weyl algebra
dc.typetext

Files

Collections

arXiv