Linear and bilinear restriction estimates for the Fourier transform

Fourier transform;Restriction theory;Wave equation;Linear restriction;Kakeya problem;Schrodingerequation

Temur, Faruk

关键词: Fourier transform;    Restriction theory;    Wave equation;    Linear restriction;    Kakeya problem;    Schrodingerequation;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/46569/Faruk_Temur.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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. Thisextends results proven by Wolff, Tao andLee-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.