{"paper":{"title":"Transmutations for Darboux transformed operators with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Sergii M. Torba, Vladislav V. Kravchenko","submitted_at":"2011-11-18T18:20:06Z","abstract_excerpt":"We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schr\\\"odinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\\\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2.\n  It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4449","kind":"arxiv","version":1},"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"}