{"paper":{"title":"Inverse formula for the Blaschke-Levy representation with applications to zonoids and sections of star bodies","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Alexander Koldobsky","submitted_at":"1996-05-09T00:00:00Z","abstract_excerpt":"We say that an even continuous function $H$ on the unit sphere $\\Omega$ in $R^n$ admits the Blaschke-Levy representation with $q>0$ if there exists an even function $b\\in L_1(\\Omega)$ so that $H^q(x)=\\int_\\Omega |(x,\\xi)|^q b(\\xi)\\ d\\xi$ for every $x\\in \\Omega.$ This representation has numerous applications in convex geometry, probability and Banach space theory. In this paper, we present a simple formula (in terms of the derivatives of $H$) for calculating $b$ out of $H.$ We use this formula to give a sufficient condition for isometric embedding of a space into $L_p$ which contributes to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9605212","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"}