{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/46569"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/46569","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Linear and bilinear restriction estimates for the Fourier transform","abstract":"This thesis is concerned with the restriction theory of the Fourier transform. We prove two restriction estimates for the Fourier transform. The first is a bilinear estimate for the light cone when the exponents are on a critical line. This extends results proven by Wolff, Tao and Lee-Vargas. The second result is a linear restriction estimate for surfaces with positive Gaussian curvature that improves over estimates proven by Bourgain and Guth, and gives the best known exponents for the well-known restriction conjecture for dimensions that are multiples of three.","abstract_html":"This thesis is concerned with the restriction theory of the Fourier transform. We prove two restriction estimates for the Fourier transform. The first is a bilinear estimate for the light cone when the exponents are on a critical line. This extends results proven by Wolff, Tao and Lee-Vargas. The second result is a linear restriction estimate for surfaces with positive Gaussian curvature that improves over estimates proven by Bourgain and Guth, and gives the best known exponents for the well-known restriction conjecture for dimensions that are multiples of three.","abstract_has_math":false,"creators":["Temur, Faruk"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Erdogan, M. Burak","Laugesen, Richard S.","Rosenblatt, Joseph","Li, Xiaochun"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-16T17:54:21Z","date_published":"2014-01-16T17:54:21Z","updated_at":"2026-07-22T22:25:36Z","subjects":["Fourier transform","Restriction theory","Wave equation","Linear restriction","Kakeya problem","Schrodinger equation"],"languages":["en"],"rights":["Copyright 2013 Faruk Temur"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/46569","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Erdogan, M. 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