{"id":"W4403245098","doi":"10.1112/blms.13165","title":"Herglotz's representation and Carathéodory's approximation","year":2024,"lang":"en","type":"article","venue":"Bulletin of the London Mathematical Society","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Science and Engineering Research Board; Department of Science and Technology, Ministry of Science and Technology, India; Ministry of Education, India; Pacific Institute for the Mathematical Sciences","keywords":"Mathematics; Holomorphic function; Representation (politics); Representation theorem; Domain (mathematical analysis); Scaling; Pure mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001637317,0.0003914789,0.0005557045,0.001286001,0.0006754906,0.001706523,0.001037848,0.0008450075,0.006010224],"category_scores_gemma":[0.003382163,0.0001640909,0.0009208552,0.001278665,0.0027995,0.003206763,0.002089613,0.00209401,0.000734175],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001349912,"about_ca_system_score_gemma":0.0005210094,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008405261,"about_ca_topic_score_gemma":0.000303697,"domain_scores_codex":[0.9992777,0.0001892393,0.00003248507,0.000152336,0.0002300591,0.000118188],"domain_scores_gemma":[0.9988012,0.0005165307,0.000136924,0.0001785548,0.0002492902,0.0001174698],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005140406,0.000004762625,0.00004458945,0.000007357171,0.000002072219,0.00001719127,0.0000776928,0.0004045621,0.000210365,0.9961818,0.0002869459,0.002757473],"study_design_scores_gemma":[0.000011158,0.00002247216,0.0001516185,0.00001197562,0.000003709974,0.00007772636,0.00006609875,0.01544637,0.0004309124,0.9796212,0.004149144,0.000007669531],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1957475,0.00161268,0.71668,0.004583266,0.0003801388,0.00006156105,0.0002586119,0.0002617481,0.08041451],"genre_scores_gemma":[0.9209572,0.0007714815,0.05811425,0.0007534564,0.0003030162,0.00009351246,0.0001207291,0.00007824488,0.01880811],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006010224,"threshold_uncertainty_score":0.02010626,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02914830638041536,"score_gpt":0.2902814131888142,"score_spread":0.2611331068083988,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}