{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:48:09Z","timestamp":1753886889156,"version":"3.41.2"},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,9]],"date-time":"2012-04-09T00:00:00Z","timestamp":1333929600000},"content-version":"vor","delay-in-days":99,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"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>Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well\u2010known d\u2032Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.<\/jats:p>","DOI":"10.1155\/2012\/761248","type":"journal-article","created":{"date-parts":[[2012,4,9]],"date-time":"2012-04-09T21:02:18Z","timestamp":1334005338000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation"],"prefix":"10.1155","volume":"2012","author":[{"given":"Gusein Sh.","family":"Guseinov","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,9]]},"reference":[{"volume-title":"Methods of Mathematical Physics. Vol. II","year":"1962","author":"Courant R.","key":"e_1_2_5_1_2"},{"volume-title":"A Course of Higher Mathematics, Vol. II","year":"1964","author":"Smirnov V. I.","key":"e_1_2_5_2_2"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-4586-9"},{"key":"e_1_2_5_4_2","doi-asserted-by":"crossref","DOI":"10.1063\/1.3062231","volume-title":"Eigenfunction Expansions Associated with Second-Order Differential Equations. Vol. 2","author":"Titchmarsh E. C.","year":"1958"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/761248.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/761248.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/761248","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:04:06Z","timestamp":1718089446000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/761248"}},"subtitle":[],"editor":[{"given":"Pablo","family":"Gonz\u00e1lez-Vera","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/761248"],"URL":"https:\/\/doi.org\/10.1155\/2012\/761248","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-09-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-30","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"761248"}}