{"id":"W2464480117","doi":"10.1016/j.aim.2016.05.027","title":"Riesz transforms and fractional integration for orthogonal expansions on spheres, balls and simplices","year":2016,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Orthogonal polynomials; Riesz transform; Invariant (physics); Polynomial; Pure mathematics; Orthogonal group; Mathematical analysis; Sobolev inequality; Laplace transform; Sobolev space","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005835256,0.0002318305,0.0004482686,0.00009693396,0.0001101418,0.00003535093,0.0001002869,0.0001012666,0.0001815123],"category_scores_gemma":[0.0007230123,0.0001292749,0.00009091239,0.0001248916,0.0001430165,0.0004363623,0.00001616888,0.0001097943,0.000003832559],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002479563,"about_ca_system_score_gemma":0.00001671995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001453286,"about_ca_topic_score_gemma":0.0001849165,"domain_scores_codex":[0.9985826,0.00003874114,0.0005812336,0.0002910814,0.0002599188,0.0002464255],"domain_scores_gemma":[0.9960018,0.003498769,0.0001460548,0.0001971646,0.00006565111,0.00009057702],"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":[0.00004106639,0.0002259175,0.00008975372,0.0004655635,0.00002876931,9.148642e-7,0.0004848132,0.000003123653,0.0006353804,0.8911608,0.00002615438,0.1068377],"study_design_scores_gemma":[0.0007374859,0.0001224383,0.00009196212,0.0004851228,0.00006111696,0.00001076293,0.0006695064,0.002517497,0.00111208,0.9914774,0.002508636,0.0002060416],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06513223,0.0003349374,0.9300921,0.0006762211,0.00004860106,0.00054602,0.00005415006,0.00004381265,0.003071952],"genre_scores_gemma":[0.5775286,0.001654626,0.4198312,0.0001011242,0.00006494351,0.0002562558,0.000006253895,0.00004707676,0.0005099947],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5123963,"threshold_uncertainty_score":0.5271679,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04224047421337955,"score_gpt":0.3768626971205025,"score_spread":0.334622222907123,"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."}}