{"id":"W2127581279","doi":"10.1090/s0002-9939-01-05928-7","title":"A direct integral decomposition of the wavelet representation","year":2001,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Wavelet; Mathematics; Representation (politics); Monomial; Dilation (metric space); Discrete wavelet transform; Real representation; Integer (computer science); Regular representation; Wavelet transform; Pure mathematics; Irreducible representation; Algebra over a field; Discrete mathematics; Combinatorics; Group (periodic table); Computer science; Artificial intelligence","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":[0.0005729049,0.0006094595,0.0005242147,0.001631446,0.0005978802,0.001677103,0.0005962043,0.0005104391,0.006951438],"category_scores_gemma":[0.001362399,0.0002245456,0.0006628335,0.0008531522,0.001374757,0.002253938,0.001277606,0.00167425,0.001504931],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005733892,"about_ca_system_score_gemma":0.0004301175,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004343542,"about_ca_topic_score_gemma":0.000307778,"domain_scores_codex":[0.9995686,0.00005946401,0.00001620925,0.00009822516,0.0001827349,0.00007471856],"domain_scores_gemma":[0.9996822,0.00005995195,0.00005177628,0.00004588547,0.00008784852,0.00007238665],"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":[0.00001688897,0.00001402478,0.00006752586,0.00002767149,0.000005179335,0.00004842724,0.0001391628,0.001001774,0.002984883,0.983704,0.000682471,0.01130789],"study_design_scores_gemma":[0.00001061762,0.00007065418,0.0003006266,0.000028403,0.00001486297,0.0002399949,0.0001491762,0.0381797,0.003060632,0.9446501,0.01327011,0.00002518613],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1202098,0.0009682501,0.8124998,0.0007090767,0.0005749034,0.00006113314,0.0001790894,0.0002005767,0.06459746],"genre_scores_gemma":[0.733669,0.002248502,0.1959144,0.0004603641,0.001147675,0.0001060191,0.0003815297,0.0004002754,0.0656723],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006951438,"threshold_uncertainty_score":0.02325493,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03740003904769841,"score_gpt":0.3580687725028463,"score_spread":0.3206687334551479,"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."}}