图书信息
图书目录
Fourier分析初步（Early Fourier Analysis）（影印版）
暂无简介
作者：
Hugh L. Montgomery
定价：
169.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-065928-3
物料号：
65928-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
分析
重点项目：
暂无
版面字数：
670.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026年
- 前辅文
- Preface
- Chapter 0. Background
- 0.1. Elementary mathematics
- 0.2. Real analysis
- 0.3. Lebesgue measure theory
- Chapter 1. Complex Numbers
- 1.1. Basics
- 1.2. Euclidean geometry via complex numbers
- 1.3. Polynomials
- 1.4. Power series
- Notes
- Chapter 2. The Discrete Fourier Transform
- 2.1. Sums of roots of unity
- 2.2. The Transform
- 2.3. The Fast Fourier Transform
- Notes
- Chapter 3. Fourier Coefficients and First Fourier Series
- 3.1. Definitions and basic properties
- 3.2. Other periods
- 3.3. Convolution
- 3.4. First Convergence Theorems
- Notes
- Chapter 4. Summability of Fourier Series
- 4.1. Cesàro summability of Fourier Series
- 4.2. Special coefficients
- 4.3. Summability
- 4.4. Summability kernels
- Notes
- Chapter 5. Fourier Series in Mean Square
- 5.1. Vector spaces of functions
- 5.2. Parseval’s Identity
- Notes
- Chapter 6. Trigonometric Polynomials
- 6.1. Sampling and interpolation
- 6.2. Bernstein’s Inequality
- 6.3. Real-valued and nonnegative trigonometric polynomials
- 6.4. Littlewood polynomials
- 6.5. Quantitative approximation of continuous functions
- Notes
- Chapter 7. Absolutely Convergent Fourier Series
- 7.1. Convergence
- 7.2. Wiener’s theorem
- Notes
- Chapter 8. Convergence of Fourier Series
- 8.1. Conditions ensuring convergence
- 8.2. Functions of bounded variation
- 8.3. Examples of divergence
- Notes
- Chapter 9. Applications of Fourier Series
- 9.1. The heat equation
- 9.2. The wave equation
- 9.3. Continuous, nowhere differentiable functions
- 9.4. Inequalities
- 9.5. Bernoulli polynomials
- 9.6. Uniform distribution
- 9.7. Positive definite kernels
- 9.8. Norms of polynomials
- Notes
- Chapter 10. The Fourier Transform
- 10.1. Definition and basic properties
- 10.2. The inversion formula
- 10.3. Fourier transforms in mean square
- 10.4. The Poisson summation formula
- 10.5. Linear combinations of translates
- Notes
- Chapter 11. Higher Dimensions
- 11.1. Multiple Discrete Fourier Transforms
- 11.2. Multiple Fourier Series
- 11.3. Multiple Fourier Transforms
- Notes
- Appendix B. The Binomial Theorem
- B.1. Binomial coefficients
- B.2. Binomial theorems
- Appendix C. Chebyshev Polynomials
- Appendix F. Applications of the Fundamental Theorem of Algebra
- F.1. Zeros of the derivative of a polynomial
- F.2. Linear differential equations with constant coefficients
- F.3. Partial fraction expansions
- F.4. Linear recurrences
- Appendix I. Inequalities
- I.1. The Arithmetic–Geometric Mean Inequality
- I.2. Hölder’s Inequality
- Notes
- Appendix L. Topics in Linear Algebra
- L.1. Familiar vector spaces
- L.2. Abstract vector spaces
- L.3. Circulant matrices
- Notes
- Appendix O. Orders of Magnitude
- Appendix T. Trigonometry
- T.1. Trigonometric functions in plane geometry
- T.2. Trigonometric functions in calculus
- T.3. Inverse trigonometric functions
- T.4. Hyperbolic functions
- References
- Notation
- Index
