{"id":"W2072840624","doi":"10.1016/j.jat.2012.05.004","title":"Relating smoothness to expressions involving Fourier coefficients or to a Fourier transform","year":2012,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Smoothness; Mathematical analysis; Fourier transform; Fourier inversion theorem; Fourier series; Pure mathematics; Trigonometric polynomial; Function (biology); Trigonometry; Fractional Fourier transform; Fourier analysis","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":[0.005122322,0.001564466,0.001177341,0.0044214,0.00144494,0.004097166,0.002080372,0.002980069,0.004872161],"category_scores_gemma":[0.03152147,0.0007247698,0.001401373,0.002588931,0.008044602,0.01406802,0.004358635,0.006587718,0.0008667434],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001113517,"about_ca_system_score_gemma":0.0007689946,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009512401,"about_ca_topic_score_gemma":0.000436464,"domain_scores_codex":[0.9977149,0.0009371925,0.0001711822,0.0003875239,0.000567514,0.000221715],"domain_scores_gemma":[0.9871655,0.007577988,0.001795368,0.001712335,0.001097252,0.000651672],"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":[0.00003564752,0.00001623887,0.0002363527,0.00004795892,0.000008719238,0.00006762647,0.0001895058,0.001294938,0.001409351,0.989976,0.0006394513,0.006078198],"study_design_scores_gemma":[0.000006470491,0.0000220216,0.0003272032,0.00002175157,0.00001611664,0.0001176996,0.0000948033,0.01550777,0.0006897331,0.9812701,0.001902854,0.00002358192],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1303576,0.002631846,0.8175712,0.00543149,0.001312568,0.00008514968,0.0002558876,0.0003838017,0.04197047],"genre_scores_gemma":[0.7798205,0.005197395,0.1807048,0.001489558,0.003382812,0.0001380725,0.0003913597,0.001224654,0.02765093],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005122322,"threshold_uncertainty_score":0.02708972,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0693644579259971,"score_gpt":0.3452382099572257,"score_spread":0.2758737520312286,"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."}}