{"id":"W1966716938","doi":"10.4153/cmb-2009-061-6","title":"On <i>L</i><sup>1</sup>-Convergence of Fourier Series under the MVBV Condition","year":2009,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Approximation Theory and Sequence Spaces","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"St. Francis Xavier University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; St. Francis Xavier University; National Science Foundation","keywords":"Mathematics; Fourier series; Monotone polygon; Sequence (biology); Series (stratigraphy); Generalization; Bounded function; Function (biology); Space (punctuation); Convergence (economics); Fourier transform; Function series; Combinatorics; Monotonic function; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"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":[0.003459053,0.0007827299,0.0007983449,0.001721803,0.0008270032,0.001841077,0.001268917,0.0008635597,0.004057098],"category_scores_gemma":[0.01202824,0.0002545187,0.0007303822,0.0007688781,0.003059561,0.002967165,0.001901111,0.00217267,0.0004712833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001634855,"about_ca_system_score_gemma":0.0008223879,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002994329,"about_ca_topic_score_gemma":0.001255029,"domain_scores_codex":[0.9990472,0.0003602211,0.00003674559,0.0001371738,0.000267023,0.0001516118],"domain_scores_gemma":[0.9941982,0.003324877,0.0005170831,0.0002454322,0.001202001,0.0005124283],"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":[0.0001068188,0.00003235673,0.001102383,0.000146461,0.0000206996,0.0002135791,0.0002974122,0.0105431,0.0064156,0.9699078,0.001254241,0.009959659],"study_design_scores_gemma":[0.00002005657,0.00009494103,0.001709428,0.0001108797,0.00001797201,0.0005036198,0.0002790332,0.2961258,0.004279973,0.6932681,0.003552675,0.00003754058],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3728307,0.004637174,0.538767,0.003443746,0.0004278389,0.0000513774,0.0002584766,0.0002508532,0.07933281],"genre_scores_gemma":[0.9484879,0.002162385,0.03624875,0.0004644205,0.0003475386,0.00009183647,0.0002217866,0.000236278,0.0117391],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004057098,"threshold_uncertainty_score":0.01829344,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.020816274810353,"score_gpt":0.2619145643538829,"score_spread":0.2410982895435299,"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."}}