{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T19:24:21Z","timestamp":1761765861677,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2014,9,12]],"date-time":"2014-09-12T00:00:00Z","timestamp":1410480000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper we study the behaviour at infinity of the Fourier transform of\nRadon measures supported by the images of fractal sets under an algorithmically\nrandom Brownian motion. We show that, under some computability conditions on\nthese sets, the Fourier transform of the associated measures have, relative to\nthe Hausdorff dimensions of these sets, optimal asymptotic decay at infinity.\nThe argument relies heavily on a direct characterisation, due to Asarin and\nPokrovskii, of algorithmically random Brownian motion in terms of the prefix\nfree Kolmogorov complexity of finite binary sequences. The study also\nnecessitates a closer look at the potential theory over fractals from a\ncomputable point of view.<\/jats:p>","DOI":"10.2168\/lmcs-10(3:20)2014","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T09:40:57Z","timestamp":1415958057000},"source":"Crossref","is-referenced-by-count":1,"title":["Fourier spectra of measures associated with algorithmically random Brownian motion"],"prefix":"10.46298","volume":"Volume 10, Issue 3","author":[{"given":"Willem Louw","family":"Fouch\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Safari","family":"Mukeru","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George","family":"Davie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2014,9,12]]},"reference":[{"key":"885:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/819\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/819\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:56:55Z","timestamp":1681243015000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/819"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,12]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-10(3:20)2014","relation":{"is-same-as":[{"id-type":"arxiv","id":"1406.3715","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1406.3715","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2014,9,12]]},"article-number":"819"}}