{"id":"https://openalex.org/W2024673934","doi":"https://doi.org/10.1137/060662472","title":"Two Variable Orthogonal Polynomials on the BiCircle and Structured Matrices","display_name":"Two Variable Orthogonal Polynomials on the BiCircle and Structured Matrices","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2024673934","doi":"https://doi.org/10.1137/060662472","mag":"2024673934"},"language":"en","primary_location":{"id":"doi:10.1137/060662472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060662472","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5110440922","display_name":"Jeffrey S. Geronimo","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]},{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeffrey S. Geronimo","raw_affiliation_strings":["Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA","School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050951828","display_name":"Hugo J. Woerdeman","orcid":"https://orcid.org/0000-0002-8538-7173"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]},{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hugo Woerdeman","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA","Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110440922"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":1.123,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.77840658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":"3","first_page":"796","last_page":"825"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973999857902527,"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"}},{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9113962650299072},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.7953602075576782},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6026301383972168},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5917755365371704},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.537514865398407},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5213814377784729},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5169605612754822},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.48564258217811584},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.4840478301048279},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4218883514404297},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.4178518056869507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39293837547302246},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3647906184196472},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36076831817626953},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3462010324001312},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11969402432441711},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11540687084197998},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1066305935382843}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9113962650299072},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7953602075576782},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6026301383972168},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5917755365371704},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.537514865398407},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5213814377784729},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5169605612754822},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.48564258217811584},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.4840478301048279},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4218883514404297},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.4178518056869507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39293837547302246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3647906184196472},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36076831817626953},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3462010324001312},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11969402432441711},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11540687084197998},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1066305935382843}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060662472","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060662472","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.239.9410","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.9410","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0612400v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W181961873","https://openalex.org/W205037048","https://openalex.org/W1953948525","https://openalex.org/W1970787953","https://openalex.org/W1983996280","https://openalex.org/W1992244412","https://openalex.org/W2030224778","https://openalex.org/W2052728940","https://openalex.org/W2055547925","https://openalex.org/W2070535943","https://openalex.org/W2091016219","https://openalex.org/W2098170360","https://openalex.org/W2106752487","https://openalex.org/W2113163466","https://openalex.org/W2120493335","https://openalex.org/W2131876911","https://openalex.org/W2143689730"],"related_works":["https://openalex.org/W2011378576","https://openalex.org/W1964907177","https://openalex.org/W2113163466","https://openalex.org/W3011177573","https://openalex.org/W2952216030","https://openalex.org/W2123451474","https://openalex.org/W2219708621","https://openalex.org/W2738354725","https://openalex.org/W3021829815","https://openalex.org/W2942902301"],"abstract_inverted_index":{"We":[0],"consider":[1],"bivariate":[2],"polynomials":[3,33,42],"orthogonal":[4,41],"on":[5,96],"the":[6,25,32,40,45,52,58,61,75,97,105],"bicircle":[7,98],"with":[8,48],"respect":[9],"to":[10,23,68,87,113],"a":[11,78,89,109],"positive":[12,79],"linear":[13,80],"functional.":[14,81],"The":[15],"lexicographical":[16,19,46,54],"and":[17,66,71],"reverse":[18,53],"orderings":[20],"are":[21,29,64,84,100,116],"used":[22,67,86],"order":[24],"monomials.":[26],"Recurrence":[27],"formulas":[28,38,63],"derived":[30,65],"between":[31,57],"of":[34,77,91,108],"different":[35],"degrees.":[36],"These":[37,82],"link":[39],"constructed":[43,50],"using":[44,51],"ordering":[47],"those":[49],"ordering.":[55],"Relations":[56],"coefficients":[59],"in":[60],"recurrence":[62],"give":[69],"necessary":[70],"sufficient":[72],"conditions":[73],"for":[74],"existence":[76],"results":[83],"then":[85],"construct":[88],"class":[90],"two":[92],"variable":[93],"measures":[94],"supported":[95],"that":[99],"given":[101],"by":[102],"one":[103],"over":[104],"magnitude":[106],"squared":[107],"stable":[110],"polynomial.":[111],"Applications":[112],"Fej\u00e9r\u2013Riesz":[114],"factorization":[115],"also":[117],"given.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
