{"id":35,"date":"2024-05-25T13:29:48","date_gmt":"2024-05-25T17:29:48","guid":{"rendered":"https:\/\/macblog.mcmaster.ca\/pobabilistic-fourier-extension-kakeya-sets\/?page_id=35"},"modified":"2025-03-17T18:59:31","modified_gmt":"2025-03-17T22:59:31","slug":"home","status":"publish","type":"page","link":"https:\/\/macblog.mcmaster.ca\/pobabilistic-fourier-extension-kakeya-sets\/","title":{"rendered":"Probabilistic Fourier Extension &amp; Kakeya Sets"},"content":{"rendered":"\n<p><em>Eric T. Sawyer, McMaster University<\/em><\/p>\n\n\n\n<p>A probabilistic Fourier extension theorem is proved that shows the extension inequality holds when averaged over all smooth Alpert multipliers. The proof uses smooth Alpert wavelets with classical techniques.<\/p>\n\n\n\n<p>This site hosts the most up-to-date version with corrected typos and invites discussion relating to the topic.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"http:\/\/macblog.mcmaster.ca\/pobabilistic-fourier-extension-kakeya-sets\/wp-content\/uploads\/sites\/177\/2025\/03\/Probabilistic-Fourier-extension-55.pdf\">Click here for the most recent version<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/arxiv.org\/abs\/2311.03145\" target=\"_blank\" rel=\"noreferrer noopener\">Click here for the version currently on the arXiv<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Eric T. Sawyer, McMaster University A probabilistic Fourier extension theorem is proved that shows the extension inequality holds when averaged<\/p>\n","protected":false},"author":382,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-35","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Probabilistic Fourier Extension &amp; Kakeya Sets - Probabilistic Fourier extension and Kakeya sets<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/macblog.mcmaster.ca\/pobabilistic-fourier-extension-kakeya-sets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probabilistic Fourier Extension &amp; Kakeya Sets - Probabilistic Fourier extension and Kakeya sets\" \/>\n<meta property=\"og:description\" content=\"Eric T. 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