{"paper":{"title":"Radial positive definite functions and Schoenberg matrices with negative eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"L. Golinskii, L. Oridoroga, M. Malamud","submitted_at":"2015-02-25T14:31:18Z","abstract_excerpt":"The main object under consideration is a class $\\Phi_n\\backslash\\Phi_{n+1}$ of radial positive definite functions on $\\R^n$ which do not admit \\emph{radial positive definite continuation} on $\\R^{n+1}$. We find certain necessary and sufficient conditions for the Schoenberg representation measure $\\nu_n$ of $f\\in \\Phi_n$ in order that the inclusion $f\\in \\Phi_{n+k}$, $k\\in\\N$, holds. We show that the class $\\Phi_n\\backslash\\Phi_{n+k}$ is rich enough by giving a number of examples. In particular, we give a direct proof of $\\Omega_n\\in\\Phi_n\\backslash\\Phi_{n+1}$, which avoids Schoenberg's theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07179","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"}