Article,
Harmonic analysis as the exploitation of symmetry--a historical survey
Bulletin (New Series) of the American Mathematical Society, 3 (1.P1): 543 -- 698 (1980)
DOI: bams/1183546470
Abstract
Preface
1. Introduction
2. The Characters of Finite Groups and the Connection with Fourier
Analysis
3. Probability Theory Before the Twentieth Century
4. The Method of Generating Functions in Probability Theory
5. Number Theory Before 1801
6. The Work of Gauss and Dirichlet and the Introduction of Characters
and Harmonic Analysis into Number Theory
7. Mathematical Physics Before 1807
8. The Work of Fourier, Poisson, and Cauchy, and Early Applications of
Harmonic Analysis to Physics
9. Harmonic Analysis, Solutions by Definite Integrals, and the Theory of
Functions of a Complex Variable
10. Elliptic Functions and Early Applications of the Theory of Functions
of a Complex Variable to Number Theory
11. The Emergence of the Group Concept
12. Introduction to Sections 13-16
13. Thermodynamics, Atoms, Statistical Mechanics, and the Old Quantum
Theory
14. The Lebesgue Integral, Integral Equations, and the Development of
Real and Abstract Analysis
15. Group Representations and Their Characters
16. Group Representations in Hilbert Space and the Discovery of Quantum
Mechanics
17. The Development of the Theory of Unitary Group Representations Be-
tween 1930 and 1945
18. Harmonie Analysis in Probability; Ergodic Theory and the Generalized
Harmonie Analysis of Norbert Wiener
19. Early Application of Group Representations to Number Theory—The
Work of Artin and Hecke
20. Idèles, Adèles, and Applications of Pontrjagin-van Kampen Duality to
Number Theory, Connections with Almost-Periodic Functions, and the
Work of Hardy and Littlewood
21. The Development of the Theory of Unitary Group Representations af-
ter 1945—A Brief Sketch with Emphasis on the First Decade
22. Applications of the General Theory
23. Summary and Conclusion
Notes
Bibliography
