{"paper":{"title":"Whitney-type extension theorems for jets generated by Sobolev functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pavel Shvartsman","submitted_at":"2016-07-06T15:09:45Z","abstract_excerpt":"Let $L^m_p(R^n)$, $p\\in [1,\\infty]$, be the homogeneous Sobolev space, and let $E\\subset R^n$ be a closed set. For each $p>n$ and each non-negative integer $m$ we give an intrinsic characterization of the restrictions to $E$ of $m$-jets generated by functions $F\\in L^{m+1}_p(R^n)$. Our trace criterion is expressed in terms of variations of corresponding Taylor remainders of $m$-jets evaluated on a certain family of \"well separated\" two point subsets of $E$. For $p=\\infty$ this result coincides with the classical Whitney-Glaeser extension theorem for $m$-jets.\n  Our approach is based on a repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01660","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"}