{"id":"W2019152887","doi":"10.5539/jmr.v4n3p50","title":"Riesz Transform on the Dual of the Laguerre Hypergroup","year":2012,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Riesz transform; Mathematics; Laguerre polynomials; M. Riesz extension theorem; Multiplier (economics); Operator (biology); Riesz potential; Fourier transform; Fractional Fourier transform; Riesz representation theorem; Singular integral; Dual (grammatical number); Integral transform; Mathematical analysis; Pure mathematics; Fourier analysis; Integral equation","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001007174,0.0006193512,0.0006895892,0.002232741,0.001042785,0.001685037,0.0006694433,0.0009281217,0.004482078],"category_scores_gemma":[0.001546135,0.0001832453,0.000701648,0.0006821023,0.00222974,0.002935987,0.001406181,0.001638772,0.0007400996],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008195255,"about_ca_system_score_gemma":0.0007626001,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005663443,"about_ca_topic_score_gemma":0.0003847087,"domain_scores_codex":[0.9995176,0.0001020148,0.0000198914,0.00009739493,0.0001600162,0.0001030964],"domain_scores_gemma":[0.9993617,0.0001098319,0.0001362019,0.00005897223,0.0001484841,0.0001848655],"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":[0.00002863984,0.00001718517,0.0001156066,0.00001744234,0.00000455074,0.00009472718,0.000105327,0.001109556,0.003558861,0.9920624,0.0001969661,0.002688702],"study_design_scores_gemma":[0.00002365104,0.000113967,0.0004629768,0.00002141777,0.000008298764,0.0002887974,0.000183317,0.03807099,0.002565326,0.9542467,0.003975927,0.00003868934],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5428708,0.00138836,0.4017165,0.001390995,0.0004664702,0.00008225059,0.0002772897,0.0001813577,0.051626],"genre_scores_gemma":[0.9329772,0.0008972528,0.04085104,0.000343076,0.0006232907,0.0001018253,0.0002607056,0.0001120908,0.0238336],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004482078,"threshold_uncertainty_score":0.01499408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3453776361494504,"score_gpt":0.4773891009159657,"score_spread":0.1320114647665153,"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."}}