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We establish equality between the essential spectrum of the Schro¨dinger operator with magnetic field in the exterior of a compact arbitrary dimensional domain and that of the operator defined in all the space, and discuss applications of this equality. .lb (A. Kachmar), email@example.com (M. Persson). Peer review under responsibility of King Saud University. Production and hosting by Elsevier 1319-5166 ª 2012 King Saud University. Production and hosting by Elsevier B.V. All rights reserved.doi:10.1016/j.ajmsc.2012.09.005 fatcat:c6vdb2y5grggdi5hcguvk3phr4