{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:45:15Z","timestamp":1759117515534},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"250","license":[{"start":{"date-parts":[[2005,5,11]],"date-time":"2005-05-11T00:00:00Z","timestamp":1115769600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We study strictly positive definite functions on the unit circle in the Euclidean space of dimension two. We develop several conditions pertaining to the determination of such functions. The major result is obtained by considering the set of real numbers as a vector space over the field of rational numbers and then applying the Kronecker approximation theorem and Weyl\u2019s criterion on equidistributions.<\/p>","DOI":"10.1090\/s0025-5718-04-01668-0","type":"journal-article","created":{"date-parts":[[2005,1,14]],"date-time":"2005-01-14T19:25:09Z","timestamp":1105730709000},"page":"709-721","source":"Crossref","is-referenced-by-count":5,"title":["Strictly positive definite functions on the unit circle"],"prefix":"10.1090","volume":"74","author":[{"given":"Xingping","family":"Sun","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,5,11]]},"reference":[{"key":"1","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0999-7","volume-title":"Modular functions and Dirichlet series in number theory","volume":"41","author":"Apostol, Tom M.","year":"1990","ISBN":"http:\/\/id.crossref.org\/isbn\/0387971270","edition":"2"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[CMS] D. Chen, V. A. Menegatto, and X. Sun, A necessary and sufficient condition for strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 131 (2003), 2733\u20132740.","DOI":"10.1090\/S0002-9939-03-06730-3"},{"key":"3","unstructured":"[M] V. A. Menegatto, Strictly positive definite functions on spheres, Ph. D. Dissertation, University of Texas-Austin, 1992."},{"key":"4","series-title":"Die Grundlehren der mathematischen Wissenschaften, Band 193","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1640-5","volume-title":"Problems and theorems in analysis. Vol. I: Series, integral calculus, theory of functions","author":"P\u00f3lya, G.","year":"1972"},{"issue":"216","key":"5","doi-asserted-by":"publisher","first-page":"1513","DOI":"10.1090\/S0025-5718-96-00780-6","article-title":"Strictly positive definite functions on spheres in Euclidean spaces","volume":"65","author":"Ron, Amos","year":"1996","journal-title":"Math. Comp.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[RS2] A. Ron and X. Sun, Strictly positive definite functions on spheres, CMS TR 94-6, University of Wisconsin-Madison, February 1994.","DOI":"10.21236\/ADA276471"},{"key":"7","first-page":"113","article-title":"Generalizaci\u00f3n del teorema de Laguerre","volume":"12","author":"Sispanov, Sergio","year":"1939","journal-title":"Bol. Mat.","ISSN":"http:\/\/id.crossref.org\/issn\/0120-0380","issn-type":"print"},{"key":"8","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1090\/gsm\/058","article-title":"The 7-15 problem","volume":"9","author":"Venkatarayudu, T.","year":"1939","journal-title":"Proc. Indian Acad. Sci., Sect. A."},{"key":"9","doi-asserted-by":"crossref","unstructured":"[W] H. Weyl, \u00dcber die Gleichverteilung von Zahlen modulo Eins, Math. Ann. 77 (1916), 313-352.","DOI":"10.1007\/BF01475864"},{"issue":"4","key":"10","doi-asserted-by":"publisher","first-page":"977","DOI":"10.2307\/2159477","article-title":"Strictly positive definite functions on spheres","volume":"116","author":"Xu, Yuan","year":"1992","journal-title":"Proc. Amer. Math. Soc.","ISSN":"http:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01668-0\/S0025-5718-04-01668-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01668-0\/S0025-5718-04-01668-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T16:14:40Z","timestamp":1682957680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01668-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,5,11]]},"references-count":10,"journal-issue":{"issue":"250","published-print":{"date-parts":[[2005,4]]}},"alternative-id":["S0025-5718-04-01668-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-04-01668-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,5,11]]}}}