{"paper":{"title":"Cardinal Interpolation With General Multiquadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeff Ledford, Keaton Hamm","submitted_at":"2015-01-08T16:42:56Z","abstract_excerpt":"This paper studies the cardinal interpolation operators associated with the general multiquadrics, $\\phi_{\\alpha,c}(x) = (\\|x\\|^2+c^2)^\\alpha$, $x\\in\\mathbb{R}^d$. These operators take the form $$\\mathscr{I}_{\\alpha,c}\\mathbf{y}(x) = \\sum_{j\\in\\mathbb{Z}^d}y_jL_{\\alpha,c}(x-j),\\quad\\mathbf{y}=(y_j)_{j\\in\\mathbb{Z}^d},\\quad x\\in\\mathbb{R}^d,$$ where $L_{\\alpha,c}$ is a fundamental function formed by integer translates of $\\phi_{\\alpha,c}$ which satisfies the interpolatory condition $L_{\\alpha,c}(k) = \\delta_{0,k},\\; k\\in\\mathbb{Z}^d$.\n  We consider recovery results for interpolation of bandlimi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01899","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"}