{"paper":{"title":"On Schroedinger operators with inverse square potentials on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Jan Derezi\\'nski, Serge Richard","submitted_at":"2016-04-12T11:05:59Z","abstract_excerpt":"The paper is devoted to operators given formally by the expression \\begin{equation*} -\\partial_x^2+\\big(\\alpha-\\frac14\\big)x^{-2}. \\end{equation*} This expression is homogeneous of degree minus 2. However, when we try to realize it as a self-adjoint operator for real $\\alpha$, or closed operator for complex $\\alpha$, we find that this homogeneity can be broken.\n  This leads to a definition of two holomorphic families of closed operators on $L^2({\\mathbb R}_+)$, which we denote $H_{m,\\kappa}$ and $H_0^\\nu$, with $m^2=\\alpha$, $-1<\\Re(m)<1$, and where $\\kappa,\\nu\\in{\\mathbb C}\\cup\\{\\infty\\}$ spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03340","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"}