{"id":491,"date":"2022-04-19T10:50:54","date_gmt":"2022-04-19T17:50:54","guid":{"rendered":"\/wp\/hades\/?p=491"},"modified":"2022-04-19T10:50:54","modified_gmt":"2022-04-19T17:50:54","slug":"bounds-for-spectral-projectors-on-riemannian-manifolds","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/04\/19\/bounds-for-spectral-projectors-on-riemannian-manifolds\/","title":{"rendered":"Bounds for spectral projectors on Riemannian manifolds"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,\u00a0<strong>April 26<\/strong>\u00a0will be at\u00a0<strong>3:30 pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<br><\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Pierre Germain<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: On a Riemannian manifold, consider the spectral projector on a thin spectral band $[\\lambda , \\lambda + \\delta]$ for the Laplace-Beltrami operator. What is its operator norm from $L^2$ to $L^q$? Or, to put it in semiclassical terms, how large can the $L^p$ norm of a quasimode normalized in $L^2$ be? This is a fascinating problem, which is closely related to a number of fundamental analytic questions. I will try and describe what is known, and some recent progress that have been made. There will be some overlap with my talk at the Analysis seminar, but not much.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0April 26\u00a0will be at\u00a03:30 pm\u00a0in\u00a0Room 740. Speaker: Pierre Germain Abstract: On a Riemannian manifold, consider the spectral projector on a thin spectral band $[\\lambda , \\lambda + \\delta]$ for the Laplace-Beltrami operator. What is its operator norm from $L^2$ to $L^q$? Or, to put it in semiclassical terms, how large can [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-491","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/491","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\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=491"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/491\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=491"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}