{"paper":{"title":"Schroedinger operators with (\\alpha\\delta'+\\beta \\delta)-like potentials: norm resolvent convergence and solvable models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Yuriy Golovaty","submitted_at":"2012-01-12T16:33:45Z","abstract_excerpt":"For real functions \\Phi and \\Psi that are integrable and compactly supported, we prove the norm resolvent convergence, as \\epsilon\\ goes to 0, of a family S(\\epsilon) of one-dimensional Schroedinger operators on the line of the form\n  S(\\epsilon)= -D^2 + \\alpha \\epsilon^{-2} \\Phi(x/\\epsilon) + \\beta \\epsilon^{-1} \\Psi(x/\\epsilon).\n  The limit results are shape-dependent: without reference to the convergence of potentials in the sense of distributions the limit operator S(0) exists and strongly depends on the pair (\\Phi,\\Psi). We show that it is impossible to assign just one self-adjoint operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2610","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"}