Composition formulas in the Weyl calculus

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. © 2009 Elsevier Inc. All rights reserved