Partial Fourier Sums and Some Probability

These are the lecture notes for a harmonic analysis reading group talk I gave October 14th, 2019 at UT Austin. They are based off of the book Classical and Multilinear Harmonic Analysis Vol. 1 by Muscalu and Schlag Throughout the following notes, we will be working on . Our Fourier transform will be defined to … Continue reading Partial Fourier Sums and Some Probability

Calderon-Zygmund Decomposition Via Martingales

This topic first came up while attending a talk by Daniel Restrepo at the UT Austin harmonic analysis learning seminar last Friday. Daniel gave a basic overview of singular integral operators, and in the process proved and used the classical Calderon-Zygmund decomposition: Theorem 1 (Calderón-Zygmund Decomposition) Given and there exists a collection of almost disjoint … Continue reading Calderon-Zygmund Decomposition Via Martingales

Topics in Complex Analysis (Solutions)

Here are my solutions to the exercises assigned for the course Topics in Complex Analysis (Math246C) during the Spring 2018 quarter at UCLA. The original course notes and exercises can be found at Dr. Tao’s Blog.   Math246C, Spring 2018 – Homework 1 Math246C, Spring 2018 – Homework 2 Math246C, Spring 2018 – Homework 3 … Continue reading Topics in Complex Analysis (Solutions)