{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:47:15Z","timestamp":1753886835029,"version":"3.41.2"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,10,15]],"date-time":"2011-10-15T00:00:00Z","timestamp":1318636800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Scientific Research fund of Zhejiang Provincial Education Department","award":["20070509","10671019"],"award-info":[{"award-number":["20070509","10671019"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20070509","10671019"],"award-info":[{"award-number":["20070509","10671019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We consider the classes of periodic functions with formal self\u2010adjoint linear differential operators <jats:italic>W<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>\u2112<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>), which include the classical Sobolev class as its special case. Using the iterative method of Buslaev, with the help of the spectrum of linear differential equations, we determine the exact values of Bernstein width of the classes <jats:italic>W<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub>(<jats:italic>\u2112<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>) in the space <jats:italic>L<\/jats:italic><jats:sub><jats:italic>q<\/jats:italic><\/jats:sub> for 1 &lt; <jats:italic>p<\/jats:italic> \u2264 <jats:italic>q<\/jats:italic> &lt; <jats:italic>\u221e<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2012\/495054","type":"journal-article","created":{"date-parts":[[2011,10,16]],"date-time":"2011-10-16T07:18:02Z","timestamp":1318749482000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bernstein Widths of Some Classes of Functions Defined by a Self\u2010Adjoint Operator"],"prefix":"10.1155","volume":"2012","author":[{"given":"Guo","family":"Feng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,10,15]]},"reference":[{"volume-title":"Some Questions in Approximation Theory","year":"1976","author":"Tikhomirov V. 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P.","year":"1985","journal-title":"Soviet Mathematics\u2014Doklady"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/495054.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/495054.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/495054","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:37:53Z","timestamp":1718087873000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/495054"}},"subtitle":[],"editor":[{"given":"Kai","family":"Diethelm","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,10,15]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/495054"],"URL":"https:\/\/doi.org\/10.1155\/2012\/495054","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2011,10,15]]},"assertion":[{"value":"2011-05-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-08-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"495054"}}