{"paper":{"title":"An application of John ellipsoids to the Szego kernel on unbounded convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Soledad Benguria","submitted_at":"2016-04-05T21:19:19Z","abstract_excerpt":"We use convex geometry tools, in particular John ellipsoids, to obtain a size estimate for the Szeg\\H{o} kernel on the boundary of a class of unbounded convex domains in $\\mathbb{C}^n.$ Given a polynomial $b:\\mathbb{R}^n \\rightarrow \\mathbb{R}$ satisfying a certain growth condition, we consider domains of the type $\\Omega_b = \\{ z\\in\\mathbb{C}^{n+1}\\,:\\, {\\rm Im}[z_{n+1}] > b({\\rm Re}[z_1],\\ldots,{\\rm Re}[z_n]) \\}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01432","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"}