Fourier级数（影印版）
作者： Rajendra Bhatia
出版时间：2022-02-28
出版社：高等教育出版社
- 高等教育出版社
- 9787040570236
- 1版
- 412513
- 46254233-3
- 精装
- 16开
- 2022-02-28
- 230
- 140
- 理学
- 数学
- 数学类
- 研究生及以上
前辅文
0 A History of Fourier Series
1 Heat Conduction and Fourier Series
1.1 The Laplace equation in two dimensions
1.2 Solutions of the Laplace equation
1.3 The complete solution of the Laplace equation
2 Convergence of Fourier Series
2.1 Abel summability and Ces`aro summability
2.2 The Dirichlet and the Fej´er kernels
2.3 Pointwise convergence of Fourier series
2.4 Term by term integration and differentiation
2.5 Divergence of Fourier series
3 Odds and Ends
3.1 Sine and cosine series
3.2 Functions with arbitrary periods
3.3 Some simple examples
3.4 Infinite products
3.5 π and infinite series
3.6 Bernoulli numbers
3.7 sin x/x
3.8 The Gibbs phenomenon
3.9 Exercises
3.10 A historical digression
4 Convergence in L2 and L1
4.1 L2 convergence of Fourier series
4.2 Fourier coefficients of L1 functions
5 Some Applications
5.1 An ergodic theorem and number theory
5.2 The isoperimetric problem
5.3 The vibrating string
5.4 Band matrices
A A Note on Normalisation
B A Brief Bibliography
Index
