傅立叶分析导论 影印本=FOURIER ANALYSIS AN INTRODUCTION

1 (p1): Chapter 1．The Genesis of Fourier Analysis
2 (p1-1): 1 The vibrating string
6 (p1-1-1): 1.1 Derivation of the wave equation
8 (p1-1-2): 1.2 Solution to the wave equation
17 (p1-1-3): 1.3 Example: the plucked string
18 (p1-2): 2 The heat equation
18 (p1-2-1): 2.1 Derivation of the heat equation
20 (p1-2-2): 2.2 Steady-state heat equation in the disc
23 (p1-3): 3 Exercises
28 (p1-4): 4 Problem
29 (p2): Chapter 2．Basic Properties of Fourier Series
30 (p2-1): 1 Examples and formulation of the problem
34 (p2-1-1): 1.1 Main definitions and some examples
39 (p2-2): 2 Uniqueness of Fourier series
44 (p2-3): 3 Convolutions
48 (p2-4): 4 Good kernels
51 (p2-5): 5 Cesàro and Abel summability: applications to Fourier series
51 (p2-5-1): 5.1 Cesàro means and summation
52 (p2-5-2): 5.2 Fejér's theorem
54 (p2-5-3): 5.3 Abel means and summation
55 (p2-5-4): 5.4 The Poisson kernel and Dirichlet's problem in the unit disc
58 (p2-6): 6 Exercises
65 (p2-7): 7 Problems
69 (p3): Chapter 3．Convergence of Fourier Series
70 (p3-1): 1 Mean-square convergence of Fourier series
70 (p3-1-1): 1.1 Vector spaces and inner products
76 (p3-2): 1.2 Proof of mean-square convergence
81 (p3-2-1): 2 Return to pointwise convergence
81 (p3-2-2): 2.1 A local result
83 (p3-2-3): 2.2 A continuous function with diverging Fourier series
87 (p3-3): 3 Exercises
95 (p3-4): 4 Problems
100 (p4): Chapter 4．Some Applications of Fourier Series
101 (p4-1): 1 The isoperimetric inequality
105 (p4-2): 2 Weyl's equidistribution theorem
113 (p4-3): 3 A continuous but nowhere differentiable function
118 (p4-4): 4 The heat equation on the circle
120 (p4-5): 5 Exercises
125 (p4-6): 6 Problems
129 (p5): Chapter 5．The Fourier Transform on ？
131 (p5-1): 1 Elementary theory of the Fourier transform
131 (p5-1-1): 1.1 Integration of functions on the real line
134 (p5-1-2): 1.2 Definition of the Fourier transform
134 (p5-1-3): 1.3 The Schwartz space
136 (p5-1-4): 1.4 The Fourier transform on S
140 (p5-1-5): 1.5 The Fourier…