Fourier分析初步（Early Fourier Analysis）（影印版）

样章

作者：

Hugh L. Montgomery

定价：

169.00 元

版面字数：

670.00千字

开本：

16开

装帧形式：

精装

页数：

408

最新
印次时间：

2026年3月

ISBN：

978-7-04-065928-3

物料号：

65928-00

出版时间：

2026年3月

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

暂无

目录
- 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