Fourier Analysis

Fourier Analysis (MATH790, SFSU)

• Lecture 01: Overview
• Lecture 02: Absolute Convergence of Fourier Series
• [Example 1] Find the Fourier Coefficients
• [Example 2] Find the Fourier Coefficients of \(f(x)=x\)
• [Example 3] Find the Fourier Coefficients of \(f(x)=\frac{(\pi-x)^2}{4}\)
• [Example 4] Find the Fourier Coefficients of \(f(x)=\frac{\pi}{\sin(\pi\alpha)}e^{i(\pi-\theta)\alpha}\)
• Lecture 03: Convolution
• Dirichlet's Test (Proof and Examples)
• Dirichlet's Kernel
• General Properties of Convolution
• Lecture 04: Good Kernels
• Lecture 05: Examples of Good Kernels