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Title:Linear and bilinear restriction estimates for the Fourier transform
Author(s):Temur, Faruk
Director of Research:Erdogan, M. Burak
Doctoral Committee Chair(s):Laugesen, Richard S.
Doctoral Committee Member(s):Erdogan, M. Burak; Rosenblatt, Joseph; Li, Xiaochun
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Fourier transform
Restriction theory
Wave equation
Linear restriction
Kakeya problem
Schrodinger equation
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.
Issue Date:2014-01-16
URI:http://hdl.handle.net/2142/46569
Rights Information:Copyright 2013 Faruk Temur
Date Available in IDEALS:2014-01-16
Date Deposited:2013-12


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