{"paper":{"title":"Multivariate Mond-Pecaric Method with Applications to Hypercomplex Function Sobolev Embedding","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Shih-Yu Chang","submitted_at":"2024-05-21T23:12:38Z","abstract_excerpt":"Mond and Pecaric introduced a method to simplify the determination of complementary inequalities for Jensen's inequality by converting it into a single-variable maximization or minimization problem of continuous functions. This principle has significantly enriched the field of operator inequalities. Our contribution lies in extending the Mond-Pecaric method from single-input operators to multiple-input operators. We commence by defining normalized positive linear maps, accompanied by illustrative examples. Subsequently, we employ the Mond-Pecaric method to derive fundamental inequalities for m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17203","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.17203/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}