{"id":"W2756595798","doi":"10.7146/math.scand.a-119120","title":"Backward shift invariant subspaces in reproducing kernel Hilbert spaces","year":2020,"lang":"en","type":"preprint","venue":"MATHEMATICA SCANDINAVICA","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Linear subspace; Mathematics; Hilbert space; Invariant (physics); Toeplitz matrix; Pure mathematics; Kernel (algebra); Reproducing kernel Hilbert space; Hardy space; Bergman space; Class (philosophy); Algebra over a field; Mathematical analysis; Computer science; Artificial intelligence","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008665766,0.0005782273,0.0004324927,0.001062894,0.0005695291,0.001516625,0.0005776525,0.000629788,0.003054114],"category_scores_gemma":[0.001480325,0.0002031827,0.0006673587,0.0006467495,0.001686841,0.002411307,0.001468955,0.001556744,0.0007919076],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005166481,"about_ca_system_score_gemma":0.0004758189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003892209,"about_ca_topic_score_gemma":0.0002000465,"domain_scores_codex":[0.9993163,0.0001956745,0.00003338357,0.00009061968,0.0002718703,0.00009219715],"domain_scores_gemma":[0.9993253,0.0001857037,0.0001053107,0.00008916231,0.0001780915,0.0001165257],"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":[0.00001135925,0.00001231881,0.0001200002,0.00002814118,0.000004659968,0.0000605276,0.000120484,0.001407557,0.003189715,0.9904963,0.0002724793,0.004276485],"study_design_scores_gemma":[0.00000975434,0.00006084393,0.0003371557,0.00001631886,0.000005191248,0.0002103315,0.00007699613,0.03198143,0.002971281,0.9587755,0.005534348,0.000020846],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2200949,0.00211125,0.7448945,0.0007045681,0.0002308426,0.00005871059,0.0002249714,0.0002428203,0.03143737],"genre_scores_gemma":[0.9160283,0.0009740975,0.06513686,0.0002121313,0.0002846617,0.00009357875,0.0003180911,0.0001404707,0.0168119],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003054114,"threshold_uncertainty_score":0.01021701,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.069191077414915,"score_gpt":0.3163285605736889,"score_spread":0.2471374831587739,"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."}}