MATH-GA.2563-001 Harmonic Analysis

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3 points

Course Description

Fourier series and integrals, Hardy-Littlewood maximal function, interpolation theory, Hilbert transform, singular integrals and Calderon-Zygmund theory, oscillatory integrals, Littlewood-Paley theory, pseudo-differential operators and Sobolev spaces. If time allows: paradifferential calculus, T1 theorem. 

Prerequisites

Real analysis; basic knowledge of complex variables and functional analysis.

Recent Offerings

TBA

Sample Exams

TBA

Recommended Texts

• Fourier Analysis by Javier Duoandikoetxea, Graduate Studies in Mathematics, AMS, 2001, as well as the lecture notes by Terry Tao