{"id":"W1993495670","doi":"10.1007/s00209-002-0479-6","title":"On a separation property of positive definite functions on locally compact groups","year":2003,"lang":"en","type":"article","venue":"Mathematische Zeitschrift","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Separation (statistics); Property (philosophy); Locally compact space; Separation property; Positive-definite matrix; Pure mathematics; Statistics; Eigenvalues and eigenvectors","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":[0.002045051,0.0008600181,0.0009861036,0.001563322,0.00192144,0.002343739,0.001210786,0.00161708,0.005962326],"category_scores_gemma":[0.005167025,0.0005190468,0.001215287,0.00121883,0.004087891,0.00916617,0.003057,0.004539306,0.0007255462],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001156031,"about_ca_system_score_gemma":0.0005419163,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005957289,"about_ca_topic_score_gemma":0.0004095144,"domain_scores_codex":[0.9994214,0.000157161,0.00002937127,0.0001250551,0.0001554464,0.0001115252],"domain_scores_gemma":[0.9957783,0.002299174,0.0004564945,0.0003689733,0.0004738872,0.0006230454],"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":[0.00008235477,0.00002398359,0.0002073792,0.00004683916,0.00000833607,0.00007183282,0.0003324317,0.0004611059,0.001828731,0.9928115,0.0007670348,0.003358397],"study_design_scores_gemma":[0.00002039356,0.00003905585,0.0003129544,0.00001042031,0.000007186796,0.00009995313,0.0001062934,0.004386948,0.0006256099,0.992952,0.001428407,0.00001069583],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5490147,0.001758068,0.3595084,0.00538109,0.0004393577,0.00005303965,0.0002584881,0.0002324939,0.08335439],"genre_scores_gemma":[0.948625,0.0008632868,0.02823666,0.000812358,0.0006700088,0.00006679413,0.0004028244,0.0001808733,0.02014222],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005962326,"threshold_uncertainty_score":0.01994592,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0504395893192673,"score_gpt":0.3455622898568379,"score_spread":0.2951227005375706,"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."}}