{"paper":{"title":"Asymptotic observability identity for the heat equation in R^d","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gengsheng Wang, Ming Wang, Yubiao Zhang","submitted_at":"2018-10-25T12:50:27Z","abstract_excerpt":"We build up an asymptotic observability identity for the heat equation in the whole space.\n  It says that one can approximately recover a solution, through observing it over some countable lattice points in the space and at one time.\n  This asymptotic identity is a natural extension of the well-known Shannon-Whittaker sampling theorem \\cite{Shannon,Whittaker}.\n  According to it, we obtain a kind of feedback null approximate controllability for impulsively controlled heat equations.\n  We also obtain a weak asymptotic observability identity with finitely many observation lattice points. This ide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10849","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"}