MATH 715: Fourier Analysis (Spring 2005)

Instructor: Camil Muscalu

Meeting Time & Room

The plan is to give an introductory course in Classical Harmonic Analysis, for graduate students.

The following topics will be covered:

(1) Tempered distributions and the Fourier transform
(2) Harmonic and subharmonic functions
(3) Boundary values of harmonic and holomorphic functions on the upper half plane
(4) Spherical harmonics
(5) Interpolation of operators
(6) Hardy-Littlewood maximal function and Littlewood-Paley square function
(7) Fractional integrals, Calderon-Zygmund theory and the Hilbert transform
(8) Poisson summation formula

We follow the classical book of Stein and Weiss, Introduction to Fourier Analysis on Euclidean Spaces, but we will sometimes deviate and use different sources. If time allows, we will cover some other topics (e.g. Kakeya Problem, Restriction Problem, Bochner-Riesz Problem, etc).

This is intended to be Part I of a one-year graduate course in Classical Harmonic Analysis.

Last modified: September 28, 2004