{"id":1614,"date":"2019-12-23T12:46:15","date_gmt":"2019-12-23T10:46:15","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1614"},"modified":"2020-01-08T18:23:58","modified_gmt":"2020-01-08T16:23:58","slug":"colloquium-tuesday-december-24-2019-speaker-itay-londner-ubc-title-optimal-arithmetic-structure-in-interpolation-sets","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1614","title":{"rendered":"Colloquium: Tuesday, December 24, 2019. Speaker: Itay Londner (UBC). Title: &#8220;Optimal arithmetic structure in interpolation sets&#8221;."},"content":{"rendered":"<p>Place:\u00a0Room 614 in the Education &amp; Sciences Building<\/p>\n<p>Time:\u00a0<strong>14:00<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><strong><u>Abstract<\/u><\/strong><strong><u>:<\/u><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)} in l^2(K) there exists a function f in L^2(S) such that its Fourier coefficients satisfy f^(k)=c(k) for all k in K.<\/p>\n<p>In the talk I will discuss the relationship between the concept of IS and the existence arithmetic structure in the set K, I will focus primarily on the case where K contains arbitrarily long arithmetic progressions with specified lengths and step sizes.<\/p>\n<p>Multidimensional analogue and recent developments on this subject will also be considered.<\/p>\n<p>This talk is based in part on joint work with Alexander Olevskii.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Place:\u00a0Room 614 in the Education &amp; Sciences Building Time:\u00a014:00 &nbsp; Abstract: &nbsp; Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data {c(k)}&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1614\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1614","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1614","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1614"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1614\/revisions"}],"predecessor-version":[{"id":1615,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1614\/revisions\/1615"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1614"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1614"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}