Localisation et developpement asymptotique des éléments du spectre conjoint d'opérateurs pseudodifferentiels qui commutent. (Localization and asymptotic development of the joint spectrum of commuting pseudodifferential operators) (Q1084320)

We consider, in \({\mathbb{R}}^ n\), p pseudodifferential operators, \(Q_ 1,...,Q_ p\), such that the sum \(\sum^{p}_{i=1}Q^ 2_ j\) is globally elliptic. We study the part of their joint spectrum \(\Lambda\) belonging to a cone C of \({\mathbb{R}}^ p\) and we localize it near a lattice Z. In the integrable case \((n=p)\) there is a unique element \(\lambda_{\tau}\) of \(\Lambda\) lying near each \(\tau\) of \(Z\cap C\), and we give an asymptotic expansion of \(\lambda_{\tau}\).