  A phase-space anisotropic operator in H=L^2(R^n) is a self-adjoint operator
whose resolvent family belongs to a natural C*-completion of the space of
H\"ormander symbols of order zero. Equivalently, each member of the resolvent
family is norm-continuous under conjugation with the Schr\"odinger unitary
representation of the Heisenberg group. The essential spectrum of such a
phase-space anisotropic operator is the closure of the union of usual spectra
of all its "phase-space asymptotic localizations", obtained as limits over
diverging ultrafilters of R^{n}\times R^n-translations of the operator. The
result extends previous analysis of the purely configurational anisotropic
operators,for which only the behavior at infinity in R^n was allowed to bo
non-trivial.
