Linear and bilinear restriction estimates for the Fourier transform

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Temur, Faruk

Contributors dc:contributor

• Erdogan, M. Burak
• Laugesen, Richard S.
• Rosenblatt, Joseph
• Li, Xiaochun

• Fourier transform
• Restriction theory
• Wave equation
• Linear restriction
• Kakeya problem
• Schrodinger equation

Statement dc:rights

• Copyright 2013 Faruk Temur

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/46569

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/46569