{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:49:09Z","timestamp":1777448949520,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:p>In this paper, we study the theory of orthogonal trigonometric polynomials (OTPs). We obtain asymptotics of OTPs with positive and analytic weight functions by Riemann\u2013Hilbert approach and find that they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, Christoffel\u2013Darboux formula and some algebraic and asymptotic properties of zeros for orthogonal trigonometric polynomials.<\/jats:p>","DOI":"10.3233\/asy-2012-1096","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:22:20Z","timestamp":1575055340000},"page":"87-132","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Orthogonal trigonometric polynomials: Riemann\u2013Hilbert analysis and relations with OPUC"],"prefix":"10.1177","volume":"79","author":[{"given":"Zhihua","family":"Du","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jinan University, Guangzhou, China. E-mail: tzhdu@jnu.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyuan","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan, China. E-mail: jydu@whu.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,9,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1096","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1096","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:33Z","timestamp":1777379973000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2012-1096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["10.3233\/ASY-2012-1096"],"URL":"https:\/\/doi.org\/10.3233\/asy-2012-1096","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}