{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:01:27Z","timestamp":1753884087227,"version":"3.37.3"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471043"],"award-info":[{"award-number":["11471043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11271263"],"award-info":[{"award-number":["11271263"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2016,11]]},"abstract":"<jats:p>This study aimed to determine the best constants in the Wirtinger inequality [Formula: see text] where [Formula: see text] is defined on [Formula: see text] with [Formula: see text]. First, we referred the computation of [Formula: see text] to the maximal eigenvalue of an integral type operator [Formula: see text]. Second, we proved that the computation of the eigenvalues of [Formula: see text] is equivalent to the solution of a Strum\u2013Liouville problem with some boundary conditions and hence we referred the computation of [Formula: see text] to finding the minimal zero of a function with one variable. Third, by comparing with a result of Lifshits, Papageorgiou, Wo\u017aniakowski, we obtained that the strong asymptotic order of [Formula: see text]: [Formula: see text].<\/jats:p>","DOI":"10.1142\/s021969131650048x","type":"journal-article","created":{"date-parts":[[2016,8,31]],"date-time":"2016-08-31T06:55:35Z","timestamp":1472626535000},"page":"1650048","source":"Crossref","is-referenced-by-count":3,"title":["The best constants in the Wirtinger inequality"],"prefix":"10.1142","volume":"14","author":[{"given":"Yongping","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenyan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, P. R. 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