{"paper":{"title":"On the Lazarev-Lieb Extension of the Hobby-Rice Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Vermont Rutherfoord","submitted_at":"2012-12-23T03:44:09Z","abstract_excerpt":"O. Lazarev and E. H. Lieb proved that given $f_{1},...,f_{n}\\in L^{1}([0,1];\\mathbb{C})$, there exists a smooth function $\\Phi$ that takes values on the unit circle and annihilates ${span}\\{f_{1},...,f_{n}}$. We give an alternative proof of that fact that also shows the $W^{1,1}$ norm of $\\Phi$ can be bounded by $5\\pi n+1$. Answering a question raised by Lazarev and Lieb, we show that if $p>1$ then there is no bound for the $W^{1,p}$ norm of any such multiplier in terms of the norms of $f_{1},...,f_{n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5759","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"}