{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:40:02Z","timestamp":1723063202692},"reference-count":0,"publisher":"Wiley","issue":"63","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"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>The behavior at infinity of the Fourier transform of the random\nmeasures that appear in the theory of multiplicative chaos of\nMandelbrot, Peyri\u00e8re, and Kahane is an area quite unexplored.\nFor context and further reference, we first present an overview\nof this theory and then the result, which is the main objective of\nthis work, generalizing a result previously announced by Kahane. We establish an estimate for the asymptotic behavior of\nthe second moment of the Fourier transform of the limit random\nmeasure in the theory of multiplicative chaos. After looking at the behavior at infinity of the Fourier\ntransform of some remarkable functions and measures, we prove a\nformula essentially due to Frostman, involving the Riesz kernels.<\/jats:p>","DOI":"10.1155\/s0161171204210183","type":"journal-article","created":{"date-parts":[[2004,11,30]],"date-time":"2004-11-30T16:22:51Z","timestamp":1101831771000},"page":"3423-3434","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the asymptotic behavior of the second moment of the Fouriertransform of a random measure"],"prefix":"10.1155","volume":"2004","author":[{"given":"Manuel L.","family":"Esqu\u00edvel","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,11,30]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/671470.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204210183","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T19:50:57Z","timestamp":1723060257000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204210183"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"63","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204210183"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204210183","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2002-10-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-11-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}