学术动态

#Math101 Session 10

Time：Nov. 22, 2021, 16:00--18:00

Location：447 Qi Xiang Building, Chang'an Campus

Speaker：Mr.Zhang,Zhenhao (Class of 2024)

Title：Revisiting Fourier series (Part III)

Abstract：This is a continuation of last week’s discussion on the theory of Fourier series. With the help of a family of approximations to the identity, we will first prove the Weierstrass approximation theorem for trigonometric polynomials, by which we can then generalize the Fourier inversion and Plancherel formulae from trigonometric polynomials to arbitrary continuous periodic functions. In particular, it will beexamined carefully in exactly what sense one has convergence of the Fourier series.At this stage, we basically follow Chapter 16 of Terence Tao’s book “Analysis II”.