目錄
Preface
Introduction
List of Symbols
Part 8: Fourier Analysis
1 The Historical Place of Fourier Analysis in Mathematics
2 Trigonometric Series and Fourier Series
3 Fourier Series and Their Coefficients
4 Pointwise Convergence and Summability
5 Fourier Series of Square Integrable Functions
6 Further Topics on the Convergence of Fourier Series
7 Holomorphic Functions, Harmonic Functions, Hardy Spaces
8 Selected Topics on Fourier Series
9 Orthonormal Expansions and Special Functions
10 The Schwartz Space
11 The Fourier Transform in S(Rn)
12 The Fourier Transform in LP-Spaces
13 The Fourier Transform of Bounded Measures
14 Selected Topics on the Fourier Transform
Part 9: Ordinary Differential Equations
15 Some Orientation-First Results
16 Basic Existence and Uniqueness Results I
17 Basic Existence and Uniqueness Results II
18 Linear Systems of First Order. Constant Coefficients
19 Linear Systems of First Order. Variable Coefficients
20 Second Order Linear Differential Equations with Real Analytic Coefficients
21 Boundary Value and Eigenvalue Problems. First Observations
22 The Hypergeometric and the Confluent Hypergeometric Differential Equation
23 Continuous Dependence on Data and Stability
24 Tangent Spaces, Tangent Bundles, and Vector Fields
25 Phase Diagrams and Flows
Part 10: Introduction to the Calculus of Variations
26 The Calculus of Variations-Setting the Scene
27 Classical Solutions of the Euler-Lagrange Equations
28 More on Local Minimisers
29 Partial Differential Equations of 1st Order
30 Aspects of Hamilton-Jacobi Theory
Appendices
Appendix I: Harmonic Analysis on Locally Compact
Abelian Groups
Appendix II: Convergence of Measures
Appendix III: Generating Functions, Orthonormal
Polynomials
Appendix IV: On Brouwer's Fixed Point Theorem
Solutions to Problems of Part 8
Solutions to Problems of Part 9
Solutions to Problems of Part 10
References
Mathematicians Contributing to Analysis (Continued)
Subject Index
編輯手記
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