{"paper":{"title":"Uncertainty principles for eventually constant sign bandlimited functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D.V. Gorbachev, S.Yu. Tikhonov, V.I. Ivanov","submitted_at":"2019-04-25T13:37:11Z","abstract_excerpt":"We study the uncertainty principles related to the generalized Logan problem in $\\mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $m\\in \\mathbb{Z}_{+}$, find \\[ \\sup\\{|x|\\colon (-1)^{m}f(x)>0\\}\\cdot \\sup \\{|x|\\colon x\\in \\mathrm{supp}\\,\\widehat{f}\\,\\}\\to \\inf, \\] where the infimum is taken over all nontrivial positive definite bandlimited functions such that $\\int_{\\mathbb{R}^d}|x|^{2k}f(x)\\,dx=0$ for $k=0,\\dots,m-1$ if $m\\ge 1$.\n  We also obtain the uncertainty principle for bandlimited functions related to the recent result by Bourgain, Cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11328","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"}