Harmonic Analysis

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Semester September 2020 - February 2021

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Schedule

Lecture

Thursday - Friday 4:00 - 6:00 pm
Online: facebook.com/HarmonicAnalysis

Problem Session

Wednesday 5:00 - 6:00 pm

Office Hour

Tuesday 6:00 - 7:00 pm

Content

This is an introductory Harmonic Analysis course, from the properties of harmonic functions and the solution to the Dirichlet problems in the ball and the upper half space, to the study of their boundary limits. We will discuss the varying techniques to solve these problems, as Fourier series and Calderón-Zygmund integrals. We will also introduce the theory of Harmonic Analysis on fractals.

Syllabus

Soon

Homework and Notes

List of assigned problem sets and announcements will be published in the Classroom page.

Text

We'll be following my manuscript (in revision): Introduction to Harmonic Analysis

Additional references

S Axler, P Bourdon & R Wade, Harmonic Function Theory, Springer

GB Folland, Introduction to Partial Differential Equations, Princeton

J Kigami, Analysis on Fractals, Cambridge

TW Körner, Fourier Analysis, Cambridge

MC Pereyra & LA Ward, Harmonic Analysis: From Fourier to Wavelets, AMS

EM Stein, Singular Integrals and Differentiability Properties of Functions, Princeton

EM Stein & R Shakarchi, Fourier Analysis: An Introduction, Princeton

EM Stein & R Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton

EM Stein & G Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton

RS Strichartz, Differential Equations on Fractals: A Tutorial, Princeton

Midterm evaluations

There will be two midterm evaluations, which will consist of assigned problems and a written essay.

Assigned problems 50%

Problems will be assigned on Friday every week, and are due by Wednesday. The problems are exercises that either will fill details of results discussed in class, or are applications of such results to other problems.

Written essay 50%

The written essay will be a report, due by the dates below, on a short research project. The project may be worked by groups of three students. Projects will be assigned by the fifth week of each midterm. Assigned projects will be different.

Calendar

• First essay due on November 18
• Second essay due on January 20

Final evaluation

The final examination will consist of a public presentation of an specific topic (50%) and an oral examination (50%).

Date

January 27, 4:00 pm