{"id":1146,"date":"2024-10-03T17:52:33","date_gmt":"2024-10-04T00:52:33","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1146"},"modified":"2024-10-09T10:03:54","modified_gmt":"2024-10-09T17:03:54","slug":"local-smoothing-for-the-hermite-wave-equation","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/10\/03\/local-smoothing-for-the-hermite-wave-equation\/","title":{"rendered":"Local smoothing for the Hermite wave equation"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>October 8th<\/strong>, will be at\u00a0<strong>2<\/strong><strong>:00pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:<\/strong> Robert Schippa<\/p>\n<p><strong>Abstract:<\/strong> We consider\u00a0<img loading=\"lazy\" decoding=\"async\" id=\"m_-5554205620027931703m_-5961278323080411372l0.6859482224822284\" class=\"CToWUd\" title=\"L^p\" src=\"https:\/\/ci3.googleusercontent.com\/meips\/ADKq_NZQrAFt0fGmtid7CGkzPJRnnTlLDxYXqyBYoLIMcZtB7RqvhmLSEmNOT15QomMjuf1-NRDMTvrpNGtz21E5ahuU6soVf6NJjgjaH8AQCNdHlUeKivP_-YJsKBbi=s0-d-e1-ft#https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=L%5Ep\" alt=\"L^p\" width=\"16\" height=\"11\" data-bit=\"iit\" \/>-smoothing estimates for the wave equation with harmonic potential. For the proof, we linearize an FIO parametrix, which yields Klein-Gordon propagation with variable mass parameter. We obtain decoupling and square function estimates depending on the mass parameter, which yields local smoothing estimates with sharp loss of derivatives. The obtained range is sharp in\u00a01D, and partial results are obtained in higher dimensions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0October 8th, will be at\u00a02:00pm\u00a0in\u00a0Room 740. Speaker: Robert Schippa Abstract: We consider\u00a0-smoothing estimates for the wave equation with harmonic potential. For the proof, we linearize an FIO parametrix, which yields Klein-Gordon propagation with variable mass parameter. We obtain decoupling and square function estimates depending on the mass parameter, which yields local [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1146","post","type-post","status-publish","format-standard","hentry","category-fall-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1146"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1146\/revisions"}],"predecessor-version":[{"id":1147,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1146\/revisions\/1147"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}