{"paper":{"title":"On the Essential Spectrum of Phase-Space Anisotropic Pseudodifferential Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.SP","authors_text":"M. Mantoiu","submitted_at":"2011-06-13T15:02:58Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2461","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}