Linear and bilinear restriction estimates for the Fourier transform

Temur, Faruk

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https://hdl.handle.net/2142/46569 Copy

Description

Title

Linear and bilinear restriction estimates for the Fourier transform

Author(s)

Temur, Faruk

Issue Date

2014-01-16T17:54:21Z

Director of Research (if dissertation) or Advisor (if thesis)

Erdogan, M. Burak

Doctoral Committee Chair(s)

Laugesen, Richard S.

Committee Member(s)

• Erdogan, M. Burak
• Rosenblatt, Joseph
• Li, Xiaochun

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2013-12

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

Copyright and License Information

Copyright 2013 Faruk Temur

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