Semester February - July 2019
Schedule
Lecture
Monday - Tuesday 4:00 - 6:00 pm
Problem Session
Friday 4:00 - 5:00 pm
Office Hour
Wednesday 4:00 - 5:00 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
Homework and Notes
List of assigned problem sets and lectures notes can be found here: Harmonic Analysis 2019
Bibliography
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
Extended bibliography
Updated as the course advances: Bibliography.pdf
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 Monday every week, and are due by Friday. The problems are exercises that either will fill details of results discussed in class, or ar 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 a student alone or in pairs. Projects will be assigned by the fifth week of each midterm. Assigned projects will be different.
Calendar
- First essay due on March 29
- Second essay due on June 7
Final evaluation
The final examination will consist of a public presentation of an specific topic (50%) and an oral examination (50%).
Date
June 25, 4:00 pm
Additional examinations
Extraordinary: July 2, 4:00 pm
Regularization: July 30, 4:00 pm