{"paper":{"title":"Schoenberg matrices of radial positive definite functions and Riesz sequences in $L^2(\\R^n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CA","authors_text":"L. Golinskii, L. Oridoroga, M. Malamud","submitted_at":"2014-03-10T13:14:04Z","abstract_excerpt":"Given a function $f$ on the positive half-line $\\R_+$ and a sequence (finite or infinite) of points $X=\\{x_k\\}_{k=1}^\\omega$ in $\\R^n$, we define and study matrices $\\kS_X(f)=\\|f(|x_i-x_j|)\\|_{i,j=1}^\\omega$ called Schoenberg's matrices. We are primarily interested in those matrices which generate bounded and invertible linear operators $S_X(f)$ on $\\ell^2(\\N)$. We provide conditions on $X$ and $f$ for the latter to hold. If $f$ is an $\\ell^2$-positive definite function, such conditions are given in terms of the Schoenberg measure $\\sigma(f)$. We also approach Schoenberg's matrices from the vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2234","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"}