{"paper":{"title":"Supersymmetry and Schr\\\"odinger-type operators with distributional matrix-valued potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Gerald Teschl, Jonathan Eckhardt, Roger Nichols","submitted_at":"2012-06-21T18:43:07Z","abstract_excerpt":"Building on work on Miura's transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schr\\\"odinger operators with matrix-valued potentials, with special emphasis on distributional potential coefficients.\n  Our principal method relies on a supersymmetric (factorization) formalism underlying Miura's transformation, which intimately connects the triple of operators $(D, H_1, H_2)$ of the form [D= (0 & A^*, A & 0) \\text{in} L^2(\\mathbb{R})^{2m} \\text{and} H_1 = A^* A, H_2 = A A^* \\text{in} L^2(\\mathbb{R})^m.] Here $A= I_m (d/dx) + \\phi$ in $L^2("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4966","kind":"arxiv","version":2},"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"}