Reduction of operators with almost periodic symbols to operators overC *-Algebras on sections of associated bundles over a torus

Abstract

A decomposition of any pseudodifferential operator σ(D) onRn with almost periodic symbol as 113-1 1 is obtained in the paper, where σA(D) is a pseudodifferential operator over a certainC*-algebraA acting on sections of a vector bundle over a torusTn whose fibre isA. The coincidence of spectra sp σ(D) = sp σA(D) is proved for all σ(D) either bounded or elliptic.