{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T04:50:39Z","timestamp":1772686239286,"version":"3.50.1"},"reference-count":4,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.<\/jats:p>","DOI":"10.1155\/2007\/20682","type":"journal-article","created":{"date-parts":[[2007,10,4]],"date-time":"2007-10-04T13:32:29Z","timestamp":1191504749000},"page":"1-3","source":"Crossref","is-referenced-by-count":2,"title":["Logarithm of the Discrete Fourier Transform"],"prefix":"10.1155","volume":"2007","author":[{"given":"Michael","family":"Aristidou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jason","family":"Hanson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","first-page":"xii+718","year":"2000"},{"key":"2","series-title":"Graduate Texts in Mathematics","first-page":"xiv+389","volume":"84","year":"1990"},{"key":"3","year":"1981"},{"key":"4","year":"2000"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/020682.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/020682.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,11]],"date-time":"2016-08-11T12:53:54Z","timestamp":1470920034000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2007\/020682\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":4,"alternative-id":["020682","20682"],"URL":"https:\/\/doi.org\/10.1155\/2007\/20682","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}