{"id":"https://openalex.org/W2964319357","doi":"https://doi.org/10.3233/asy-2012-1096","title":"Orthogonal trigonometric polynomials: Riemann\u2013Hilbert analysis and relations with OPUC","display_name":"Orthogonal trigonometric polynomials: Riemann\u2013Hilbert analysis and relations with OPUC","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2964319357","doi":"https://doi.org/10.3233/asy-2012-1096","mag":"2964319357"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2012-1096","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1096","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101275662","display_name":"Zhihua Du","orcid":null},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihua Du","raw_affiliation_strings":["Department of Mathematics, Jinan University, Guangzhou, China. E-mail: tzhdu@jnu.edu.cn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jinan University, Guangzhou, China. E-mail: tzhdu@jnu.edu.cn","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045243209","display_name":"Jinyuan Du","orcid":"https://orcid.org/0000-0002-2878-2863"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinyuan Du","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, China. E-mail: jydu@whu.edu.cn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, China. E-mail: jydu@whu.edu.cn","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101275662"],"corresponding_institution_ids":["https://openalex.org/I159948400"],"apc_list":null,"apc_paid":null,"fwci":0.4143,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66272189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"79","issue":"1-2","first_page":"87","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6900536417961121},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.6844902038574219},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6711035370826721},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5729551911354065},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5254896283149719},{"id":"https://openalex.org/keywords/trigonometric-substitution","display_name":"Trigonometric substitution","score":0.43057286739349365},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37027767300605774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3300562798976898},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.07851305603981018}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6900536417961121},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6844902038574219},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6711035370826721},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5729551911354065},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5254896283149719},{"id":"https://openalex.org/C9317044","wikidata":"https://www.wikidata.org/wiki/Q1191963","display_name":"Trigonometric substitution","level":5,"score":0.43057286739349365},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37027767300605774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3300562798976898},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.07851305603981018},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.0},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-2012-1096","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1096","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W99540309","https://openalex.org/W181961873","https://openalex.org/W637897940","https://openalex.org/W1488341329","https://openalex.org/W1504035215","https://openalex.org/W1544715525","https://openalex.org/W1646417519","https://openalex.org/W1811306811","https://openalex.org/W2022559404","https://openalex.org/W2040477106","https://openalex.org/W2082829459","https://openalex.org/W2092264187","https://openalex.org/W2383462528","https://openalex.org/W2592226177","https://openalex.org/W2798896096","https://openalex.org/W3037482517","https://openalex.org/W3038928148","https://openalex.org/W3101059220","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W164200052","https://openalex.org/W1483355072","https://openalex.org/W2898978554","https://openalex.org/W4289328889","https://openalex.org/W3022244109","https://openalex.org/W579400037","https://openalex.org/W2981512670","https://openalex.org/W3104094566","https://openalex.org/W3022590230","https://openalex.org/W4387010780"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,48],"study":[4],"the":[5,36,41,44],"theory":[6,45],"of":[7,15,46,62],"orthogonal":[8,33,65],"trigonometric":[9,66],"polynomials":[10,34],"(OTPs).":[11],"We":[12],"obtain":[13],"asymptotics":[14],"OTPs":[16],"with":[17,32],"positive":[18],"and":[19,26,43,56,59],"analytic":[20],"weight":[21],"functions":[22],"by":[23],"Riemann\u2013Hilbert":[24],"approach":[25],"find":[27],"that":[28],"they":[29],"have":[30],"relations":[31,42],"on":[35],"unit":[37],"circle":[38],"(OPUC).":[39],"By":[40],"OPUC,":[47],"also":[49],"get":[50],"four-terms":[51],"recurrent":[52],"formulae,":[53],"Christoffel\u2013Darboux":[54],"formula":[55],"some":[57],"algebraic":[58],"asymptotic":[60],"properties":[61],"zeros":[63],"for":[64],"polynomials.":[67]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}