{"paper":{"title":"Circle packing and interpolation in Fock spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Stevenson, Kehe Zhu","submitted_at":"2013-02-14T17:43:31Z","abstract_excerpt":"It was shown by James Tung in 2005 that if a sequence $Z=\\{z_n\\}$ of points in the complex plane satisfies $$\\inf_{n\\not=m}|z_n-z_m|>2/\\sqrt\\alpha,$$ then $Z$ is a sequence of interpolation for the Fock space $F^p_\\alpha$. Using results from circle packing, we show that the constant above can be improved to $$\\sqrt{2\\pi/(\\sqrt3\\,\\alpha)},$$ which is strictly smaller than $2/\\sqrt\\alpha$. A similar result will also be obtained for sampling sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3487","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"}