{"paper":{"title":"Positive Definite Functions on Complex Spheres and their Walks through Dimensions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ana Paula Peron, Emilio Porcu, Eugenio Massa","submitted_at":"2017-04-05T01:31:29Z","abstract_excerpt":"We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Mont\\'ee and Descente operators as proposed by Beatson and zu Castell [J. Approx. Theory 221 (2017), 22-37] on the basis of the original Matheron operator [Les variables r\\'egionalis\\'ees et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Mont\\'ee operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01237","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"}