## Approximations semi-classiques du spectre de systèmes différentiels asymptotiques.(French)Zbl 0535.58040

The author generalizes results on spectral properties of selfadjoint asymptotic differential equations [see the author, Journ. ”Equations Dériv. Partielles”, St.-Jean-De-Monts 1982, Conf. No.14 (1982; Zbl 0497.58023)] to asymptotic systems. At first a brief survey on the symbol calculus is given. Then this calculus is adapted to selfadjoint asymptotic differential systems. The author derives asymptotic approximations of their spectrum. As an example a (2$$\times 2)-system$$, namely the reduced Dirac-equation for the atom with one electron in a constant magnetic field, is treated.
Reviewer: K.H.Jansen

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58J40 Pseudodifferential and Fourier integral operators on manifolds 35P15 Estimates of eigenvalues in context of PDEs

Zbl 0497.58023