{"id":"W2200365580","doi":"10.1215/20088752-3320401","title":"A group structure on $\\mathbb{D}$ and its application for composition operators","year":2016,"lang":"en","type":"article","venue":"Annals of Functional Analysis","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Unimodular matrix; Automorphism; Group (periodic table); Equivalence (formal languages); Pure mathematics; Automorphism group; Sequence (biology); Composition (language); Physics","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":[0.002358791,0.001245292,0.001330591,0.00403042,0.003645495,0.00326054,0.001577419,0.003199447,0.01146295],"category_scores_gemma":[0.004677936,0.0007254211,0.002354228,0.002466733,0.007078412,0.008695558,0.005796648,0.004859658,0.001548373],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00160343,"about_ca_system_score_gemma":0.000966956,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009463627,"about_ca_topic_score_gemma":0.0008329941,"domain_scores_codex":[0.9987856,0.0004503224,0.00007390177,0.000265098,0.0002492416,0.0001758603],"domain_scores_gemma":[0.9978688,0.0009929413,0.0001833881,0.000208218,0.0003017788,0.0004448677],"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":[0.00001064157,0.00001221703,0.00003158674,0.0000103363,0.000002576905,0.00003722737,0.0001175811,0.0001651224,0.0002942961,0.9965841,0.0003757501,0.002358564],"study_design_scores_gemma":[0.000006931917,0.00001210664,0.00004395859,0.000007403799,0.000004552096,0.00006152924,0.00005791764,0.003671666,0.0002455515,0.9931404,0.002738185,0.000009784962],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.123596,0.001703887,0.7661749,0.006219299,0.002677202,0.0001104798,0.0002420968,0.0004040386,0.09887197],"genre_scores_gemma":[0.699949,0.002136234,0.2202676,0.001987122,0.003375195,0.0003228146,0.0002904923,0.0007337013,0.07093787],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01146295,"threshold_uncertainty_score":0.03834742,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06369002323182552,"score_gpt":0.3209061536753389,"score_spread":0.2572161304435134,"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."}}