2008-8-20 Stein Analysis 暑期讨论班

我们的Stein Analysis暑期讨论班会在8月20-8月30日之间举行。每天

下午 2:00-4:30 中间休息+讨论 30分钟
晚上 7:00-9:30 中间休息+讨论 30分钟

演讲者与演讲内容：

马欣欣：Complex Analysis， Chapter 9,10

Chapter 9 An Introduction to Elliptic Functions
In this chapter, we will study doubly-periodic functions (called elliptic function). We will learn Weierstrass Function and go as far as to glimpse a possible connection with number theory, by considering the Eisenstein series and their expression involving division functions.

1. Liouville's theorems
2. The process of constructing Weierstrass Function
3. Properties of Weierstrass Function
4. Theorem 2.5

Chapter 10 Applications of Theta function
This chapter is devoted to a closer look at the theory of Theta functions and some of its applications to combinatolics and number theory.

1. Product formula Theorem
2. Proposition 2.2
3. The two-squares theorem
4. The four squares theorem


耿佩：Fourier Analysis, Chapter 7

The goal here is to introduce another version of Fourier analysis, now for functions defined on finite sets (finite abelian groups). We begin with the simplest example Z(N). The computation of the Fourier coefficients lead to "the fast Fourier transform". Then we will undertake the more general theory of Fourier analysis on finite abelian groups.

1. Theorem 1.2 Fourier transform of functions on Z(N)
2. Theorem 1.3 Fast Fourier transform
3. Properties of characters
4. Fourier inversion and Plancherel formula

然后会她俩累的时候穿插一些小单元：

1. 肖一晨复习： Entire function and Hadamard product (Complex Analysis Chapter 5,6)
2. 段红伟复习： Paley-Wiener theorem(Chapter 4)
3. 林义筌报告：Besov space and The Heat equation
4. 郝进宏 等周不等式