{"id":"W2002892553","doi":"10.1006/jfan.2000.3612","title":"A Separation Property of Positive Definite Functions on Locally Compact Groups and Applications to Fourier Algebras","year":2000,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Property (philosophy); Locally compact space; Positive-definite matrix; Separation property; Fourier transform; Pure mathematics; Separation (statistics); Locally compact group; Algebra over a field; Mathematical analysis; Statistics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001920955,0.0006340397,0.0009248154,0.001718134,0.001498079,0.002192794,0.0009824123,0.001489576,0.00481778],"category_scores_gemma":[0.005141543,0.0004564031,0.0011283,0.00108757,0.003370082,0.006591008,0.002394696,0.002904209,0.0005233031],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007352053,"about_ca_system_score_gemma":0.0005240364,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004643102,"about_ca_topic_score_gemma":0.0004085269,"domain_scores_codex":[0.9994336,0.000152973,0.00003676576,0.0001274106,0.0001584169,0.0000907907],"domain_scores_gemma":[0.9961632,0.001840635,0.0005056469,0.0003691497,0.0005394747,0.0005818586],"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":[0.00003494471,0.00002324002,0.000177771,0.00002732768,0.000006435801,0.0000667735,0.0002127192,0.0004312206,0.002053743,0.992167,0.0004869172,0.004311998],"study_design_scores_gemma":[0.00001497251,0.00002344073,0.0002244203,0.000007625259,0.000005382833,0.000149336,0.00008649212,0.007519698,0.0006586971,0.9900176,0.001279349,0.00001307124],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3640321,0.001355535,0.5881098,0.002688313,0.0003480494,0.00004402143,0.0001474728,0.0002063206,0.04306842],"genre_scores_gemma":[0.9298695,0.00070292,0.05255077,0.0004983979,0.0006276217,0.00005313663,0.0002081471,0.0001309554,0.01535854],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00481778,"threshold_uncertainty_score":0.0161171,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04088811283512553,"score_gpt":0.3396419984183462,"score_spread":0.2987538855832207,"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."}}