{"paper":{"title":"On two natural extensions of Vinnicombe's metric: their noncoincidence yet equivalence on stabilizable plants over A_+","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.OC","authors_text":"Amol Sasane, Rudolf Rupp","submitted_at":"2011-11-10T12:50:59Z","abstract_excerpt":"Let A_+ be the ring of Laplace transforms of complex Borel measures on R with support in [0,+\\infty) which do not have a singular nonatomic part. We compare the nu-metric d_{A_+} for stabilizable plants over A_+ given in the article by Ball and Sasane [2010], with yet another metric d_{H^\\infty}|_{A_+}, namely the one induced by the metric d_{H^\\infty} for the set of stabilizable plants over H^\\infty given in teh article by Sasane in 2011. Both d_{A_+} and d_{H^\\infty} coincide with the classical Vinnicombe metric defined for rational transfer functions, but we show here by means of an example"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2467","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"}