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Erdogan, M. Burak Laugesen, Richard S. Erdogan, M. Burak Rosenblatt, Joseph Li, Xiaochun Temur, Faruk 2014-01-16T17:54:21Z 2014-01-16T17:54:21Z 2013-12 2014-01-16T17:54:21Z 2013-12 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-07-29T19:56:54Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 6 Temur_Faruk.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) Temur_Faruk.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) Temur_Faruk.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) Temur_Faruk.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) Temur_Faruk.pdf: 1407810 bytes, checksum: 66f7b483cd4820e641356d582150dd14 (MD5) Temur_Faruk.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) Made available in DSpace on 2014-01-16T17:54:21Z (GMT). No. of bitstreams: 2 Faruk_Temur.pdf: 1407436 bytes, checksum: 69c4d6a7602e9298e91be1eeeba36606 (MD5) license.txt: 4059 bytes, checksum: c89dc95f87c647b5b83cd09dfcf482bb (MD5) http://hdl.handle.net/2142/46569 en Copyright 2013 Faruk Temur Fourier transform Restriction theory Wave equation Linear restriction Kakeya problem Schrodinger equation Linear and bilinear restriction estimates for the Fourier transform text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD