Composition formulas in the Weyl calculus

Toshiyuki Kobayashi (1) , Bent Orsted (2) , Michael Pevzner (3) , André Unterberger (3)

1 Graduate School of Mathematics
2 Mathematical Institute
3 LMR - Laboratoire de Mathématiques de Reims

In pseudodifferential analysis, the usual composition formula, which has asymptotic value, extends that valid for differential operators. The one developed here is based instead on the decomposition of symbols (functions in Rn × Rn) as integral superpositions of homogeneous ones, of degrees lying on the complex line with real part −n. It extends the one known in the one-dimensional case in connection with automorphic pseudodifferential analysis.

Mots clés: Weyl calculus; Composition formulas; Principal series representations; Automorphic symbols and triple products

Domaines: Théorie des représentations [math.RT]

Toshiyuki Kobayashi, Bent Orsted, Michael Pevzner, André Unterberger. Composition formulas in the Weyl calculus. Journal of Functional Analysis, 2009, 257, pp.948-991. ⟨10.1016/j.jfa.2008.12.023⟩. ⟨hal-00395826⟩