{"paper":{"title":"Singular continuous spectrum of half-line Schr\\\"odinger operators with point interactions on a sparse set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Vladimir Lotoreichik","submitted_at":"2010-11-10T19:12:22Z","abstract_excerpt":"We say that a discrete set $X =\\{x_n\\}_{n\\in\\dN_0}$ on the half-line $$0=x_0 < x_1 <x_2 <x_3<... <x_n<... <+\\infty$$ is sparse if the distances $\\Delta x_n = x_{n+1} -x_n$ between neighbouring points satisfy the condition $\\frac{\\Delta x_{n}}{\\Delta x_{n-1}} \\rightarrow +\\infty$. In this paper half-line Schr\\\"odinger operators with point $\\delta$- and $\\delta^\\prime$-interactions on a sparse set are considered. Assuming that strengths of point interactions tend to $\\infty$ we give simple sufficient conditions for such Schr\\\"odinger operators to have non-empty singular continuous spectrum and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2459","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"}