{"id":"W4232586095","doi":"10.1007/978-1-4612-1258-4_3","title":"Positive Operator-Valued Measures and Frames","year":2000,"lang":"en","type":"book-chapter","venue":"Graduate texts in contemporary physics","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"","keywords":"Hilbert space; Operator (biology); Kernel (algebra); Connection (principal bundle); Algebra over a field; Reproducing kernel Hilbert space; Mathematics; Pure mathematics; Calculus (dental); Group (periodic table); Computer science","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":[0.0006556123,0.0009689213,0.000571651,0.001714006,0.001371084,0.003611968,0.0006092637,0.001183554,0.008701737],"category_scores_gemma":[0.001272305,0.0003622114,0.0002841994,0.002122553,0.003647356,0.005637368,0.0009063001,0.002213556,0.001391281],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001700041,"about_ca_system_score_gemma":0.0005868549,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005867589,"about_ca_topic_score_gemma":0.0007590457,"domain_scores_codex":[0.9997124,0.00009086957,0.00001490187,0.00004713442,0.0001078514,0.00002686996],"domain_scores_gemma":[0.9996156,0.0001897711,0.00003062356,0.00003897697,0.00009020236,0.00003486404],"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":[8.697003e-7,0.000002243251,0.000005901978,0.000009908624,6.048538e-7,0.000004780329,0.0000822009,0.00003721322,0.00006861478,0.9948513,0.002332679,0.002603752],"study_design_scores_gemma":[0.000001512289,0.000002944328,0.00004338429,0.00001513678,0.000001322048,0.00003239272,0.00005732645,0.0001912356,0.00006148224,0.9688488,0.03074162,0.000002868532],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01732189,0.03142247,0.06356896,0.006815847,0.002341257,0.00002876872,0.0001664009,0.0001364287,0.878198],"genre_scores_gemma":[0.5102261,0.03451934,0.02751449,0.00182472,0.006531862,0.0002095333,0.0002953625,0.0002594044,0.4186191],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.008701737,"threshold_uncertainty_score":0.02911025,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1566593963172906,"score_gpt":0.3275768480973762,"score_spread":0.1709174517800856,"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."}}