 1190 Marius Mantoiu
 On the Essential Spectrum of PhaseSpace Anisotropic Pseudodifferential Operators
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Jun 13, 11

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Abstract. A phasespace anisotropic operator in H=L^2(R^n) is a selfadjoint 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 normcontinuous
under conjugation with the Schr\"odinger unitary representation of the Heisenberg group.
The essential spectrum of such a phasespace anisotropic operator is the closure of the union of usual spectra of all its "phasespace
asymptotic localizations", obtained as limits over diverging ultrafilters of R^{2n}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 nontrivial.
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