{"id":"W2319140647","doi":"10.4064/bc88-0-6","title":"Fourier–Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group","year":2010,"lang":"en","type":"article","venue":"Banach Center Publications","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Heisenberg group; Fourier transform; Mathematics; Group (periodic table); Laplace operator; Pure mathematics; Mathematical physics; Physics; Mathematical analysis; Quantum mechanics","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":[0.0008931576,0.001076128,0.0005351818,0.00186196,0.0008051094,0.001723537,0.0006684329,0.0008338479,0.004455878],"category_scores_gemma":[0.001960674,0.0002467546,0.0009462874,0.0009315995,0.002813762,0.003541674,0.0013468,0.002297516,0.0007534206],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008581807,"about_ca_system_score_gemma":0.0004850185,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007637092,"about_ca_topic_score_gemma":0.0004805777,"domain_scores_codex":[0.9997618,0.00005591721,0.00001101383,0.00004730324,0.00008110706,0.00004286708],"domain_scores_gemma":[0.9994335,0.0001929416,0.000104248,0.00007716322,0.0001079909,0.00008416778],"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":[0.000006301586,0.000005806125,0.0000711877,0.00000827345,0.000003892969,0.00005157354,0.0001119147,0.001110516,0.001341476,0.9946429,0.0004655792,0.002180603],"study_design_scores_gemma":[0.000004026617,0.00000913999,0.0001781832,0.00000541068,0.000003290547,0.00008497664,0.00005769296,0.01330985,0.0007128941,0.9843412,0.001284022,0.000009331172],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3696516,0.001275369,0.5245163,0.003537613,0.0005192854,0.0000618198,0.0002764431,0.0002521133,0.09990953],"genre_scores_gemma":[0.9014956,0.001687273,0.0512262,0.0006035886,0.0007524975,0.0001120892,0.0002451715,0.0002177922,0.04365971],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004455878,"threshold_uncertainty_score":0.01490635,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04917125884068739,"score_gpt":0.3201799869955074,"score_spread":0.27100872815482,"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."}}