Let X be a symmetric space of noncompact type whose isometry group is either SU(n, 1) or Spin(2n, 1). Then the Dirac operator D is defined on L2-sections of certain homogeneous vector bundles over X.

We introduce a class of matrix valued pseudo-differential operators that admit scalar locally conjugate operators (in the sense of E. Mourre) and we give a general method of study of singular ...