\t\t\t\tThe next Analysis and PDE seminar will take place Monday, October 15, from 4-5pm in 740 Evans.<\/p>\n
Title: The effect of threshold energy obstructions on the $L^1 \\to L^\\infty$
\ndispersive estimates for some Schr\u00f6dinger type equations<\/p>\n
Abstract: In this talk, I will discuss the differential equation $iu_t
\n= Hu, H := H_0 + V$ , where $V$ is a decaying potential and $H_0$ is a
\nLaplacian related operator. In particular, I will focus on when $H_0$
\nis Laplacian, Bilaplacian and Dirac operators. I will discuss how the
\nthreshold energy obstructions, eigenvalues and resonances, effect the
\n$L^1 \\to L^\\infty$ behavior of $e^{itH} P_{ac} (H)$. The threshold
\nobstructions are known as the distributional solutions of $H\\psi = 0$
\nin certain dimension dependent spaces. Due to its unwanted effects on
\nthe dispersive estimates, its absence have been assumed in many
\nwork. I will mention our previous results on Dirac operator and recent
\nresults on Bilaplacian operator under different assumptions on
\nthreshold energy obstructions.\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"
The next Analysis and PDE seminar will take place Monday, October 15, from 4-5pm in 740 Evans. Title: The effect of threshold energy obstructions on the $L^1 \\to L^\\infty$ dispersive estimates for some Schr\u00f6dinger type equations Abstract: In this talk, I will discuss the differential equation $iu_t = Hu, H := H_0 + V$ , […]<\/p>\n","protected":false},"author":108,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-595","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/108"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=595"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/595\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}