{"paper":{"title":"Schoenberg Representations and Gramian Matrices of Mat\\'ern Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dohie Kim, Hera Yun, Kyungwon Park, Yong-Kum Cho","submitted_at":"2017-02-20T08:32:09Z","abstract_excerpt":"We represent Mat\\'ern functions in terms of Schoenberg's integrals which ensure the positive definiteness and prove the systems of translates of Mat\\'ern functions form Riesz sequences in $L^2(\\R^n)$ or Sobolev spaces. Our approach is based on a new class of integral transforms that generalize Fourier transforms for radial functions. We also consider inverse multi-quadrics and obtain similar results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05894","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"}