{"id":"W73953985","doi":"10.1007/978-3-7643-8969-7_3","title":"Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group","year":2008,"lang":"en","type":"book-chapter","venue":"Birkhäuser Basel eBooks","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Heisenberg group; Laplace operator; Heat equation; Group (periodic table); Mathematical physics; Mathematics; Pure mathematics; Physics; Mathematical analysis; Quantum mechanics","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":[0.0004709811,0.0006095524,0.0003990984,0.0008408862,0.0005272462,0.001256827,0.0006056718,0.0009049355,0.002689572],"category_scores_gemma":[0.0008250169,0.0002360534,0.0006392846,0.0007141709,0.002248474,0.002972814,0.0008028231,0.002235432,0.0006300074],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009282385,"about_ca_system_score_gemma":0.0006125949,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008454923,"about_ca_topic_score_gemma":0.0007355083,"domain_scores_codex":[0.9998502,0.00002860583,0.00000849515,0.00002329433,0.00006614444,0.00002328829],"domain_scores_gemma":[0.9998135,0.00007306047,0.00002273179,0.00002345608,0.00004171962,0.00002550357],"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":[0.00000327689,0.000003848235,0.00001498152,0.00001413263,0.000001639664,0.00002270869,0.00008469874,0.0006718765,0.00103869,0.9949267,0.0005452663,0.002672297],"study_design_scores_gemma":[0.00000304442,0.00001034211,0.00007563375,0.000008325812,0.00000192802,0.00006272177,0.00004396125,0.005876207,0.0006922846,0.9881949,0.005023876,0.000006712447],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2131716,0.01264355,0.4702527,0.007101433,0.002212888,0.00008556039,0.0002738191,0.0003293473,0.293929],"genre_scores_gemma":[0.7274141,0.008255385,0.07335099,0.0008003878,0.001495474,0.0001336588,0.0002236784,0.0002761101,0.1880502],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002689572,"threshold_uncertainty_score":0.0089975,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08763066046946523,"score_gpt":0.26957936386509,"score_spread":0.1819487033956248,"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."}}