{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T18:10:03Z","timestamp":1719511803169},"reference-count":0,"publisher":"Wiley","issue":"66","license":[{"start":{"date-parts":[[2004,12,14]],"date-time":"2004-12-14T00:00:00Z","timestamp":1102982400000},"content-version":"vor","delay-in-days":348,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Centre of Mathematics of the University of Porto"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We establish the inverse Lebedev expansion with respect to\nparameters and arguments of the modified Bessel functions for an\narbitrary function from Hardy\u2032s space <jats:italic>H<\/jats:italic><jats:sub>2,<jats:italic>A<\/jats:italic><\/jats:sub>, <jats:italic>A<\/jats:italic> &gt; 0. This gives another version of the Fourier\u2010integral\u2010type theorem for\nthe Lebedev transform. The result is generalized for a weighted\nHardy space , 0 &lt; <jats:italic>A<\/jats:italic> &lt; 1, of analytic functions <jats:italic>f<\/jats:italic>(<jats:italic>z<\/jats:italic>), <jats:italic>z<\/jats:italic> = Re<jats:italic>z<\/jats:italic> + <jats:italic>i<\/jats:italic><jats:italic>\u03c4<\/jats:italic>, in the strip |Re<jats:italic>z<\/jats:italic>| \u2264 <jats:italic>A<\/jats:italic>. Boundedness and inversion properties\nof the Lebedev transformation from this space into the space\n<jats:italic>L<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>\u211d<\/jats:italic><jats:sub>+<\/jats:sub>; <jats:italic>x<\/jats:italic><jats:sup>\u22121<\/jats:sup><jats:italic>d<\/jats:italic><jats:italic>x<\/jats:italic>) are considered. When Re<jats:italic>z<\/jats:italic> = 0, we derive the familiar Plancherel theorem for the\nKontorovich\u2010Lebedev transform.<\/jats:p>","DOI":"10.1155\/s0161171204301365","type":"journal-article","created":{"date-parts":[[2007,4,26]],"date-time":"2007-04-26T12:27:11Z","timestamp":1177590431000},"page":"3603-3616","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Lebedev transformation in Hardy\u2032s spaces"],"prefix":"10.1155","volume":"2004","author":[{"given":"Semyon B.","family":"Yakubovich","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,12,14]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/194526.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204301365","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T17:36:39Z","timestamp":1719509799000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204301365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"66","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204301365"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204301365","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-01-31","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-12-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}