Representations of almost periodic pseudodifferential operators and\n applications in spectral theory

The paper concerns algebras of almost periodic pseudodifferential operators\non $\\mathbb R^d$ with symbols in H\\"ormander classes. We study three\nrepresentations of such algebras, one of which was introduced by Coburn, Moyer\nand Singer and the other two inspired by results in probability theory by\nGladyshev. Two of the representations are shown to be unitarily equivalent for\nnonpositive order. We apply the results to spectral theory for almost periodic\npseudodifferential operators acting on $L^2$ and on the Besicovitch Hilbert\nspace of almost periodic functions.\n