《复分析》已被哈佛大学和加利福尼亚理工学院选为教材。与《复分析》相配套的教材《傅立叶分析导论》和《实分析》也已影印出版。 |
| SteIn在国际上享有盛誉，现任美国普林斯顿大学数学系教授。他是当代分析，特别是调和分析领域领袖人物之一。古典调和分析最困难问题之一是推广到多维。他是多维欧氏调和分析的创造者之一，为此他发展了许多先进工具，如奇异积分、Radon变换、极大函数等。他还发展了多个实变元的Hardy空间理论，推广了1971年F J0hn和L.Nirenberg的重要发现：即Hardy空间与 BMO空间的对偶。他在群上的调和分析方面也有贡献，例如同R.Kunze一起发现所谓Kunze-stein现象。除此之外，他对多复变问题也做出了突出成绩。.. << 查看详细 |
| foreword introductlon chapter 1．preliminaries to complex analysis l complex numbers and the eompicx plane 1.1 basic properties l.2 convergence 1.3 sets in tim complex plane 2 functions on the complex plane 2.l conltinuous fnetions 2.2 holomorphic fimctions 2.3 p0wei series 3 integration along crvcs 4 exorcises chapter 2 cauchy’s theorem and its applications 1 goursat’s theorem 2 local existencc of primitives and cauchy s theorem in a disc 3 evaiuatlon of some integrals 4 cauchy’s integral formulas 5 1lrther applications .5.1 morera’s timorem 5.2 sequences of holomorphic functions 5.3 holomorphic functions defined in terms of integrals 5.4 schwarz reflection principle 5.5 runge’s approxlnlatlon theorem 6 exereises 7 problems chapter 3．meromorphic functions and the logarithm 1 zeros and polcs 2 the residue formuia 2.l examples 3 singularities and meromorphic functions 4 the argmuent principle and applications 5 homotopies and simply connected domains 6 the complex logarithm 7 fourier series and harmonic functions 8 exercises 9 problenis chapter 4. the fourier transforin 1 the class 2 action of the fourier transform on 3 palev-wiener tbeorem 4 exercises 5 problems chapter 5. entire functions 1 jensen's formula 2 functions of finite order 3 infinite products 3.1 generalities 3.2 example: the product foemula for the sine function 4 weierstrass infinite products 5 hadamard's factorozatoon theorem 6 exercises 7 problems chapter 6. the gamma and zeta functions 1 the gamma function 1.1 analytic continuation 1.2 furtiicr properties of f 2 the zeta function 2.1 functional equation and analytic continuation 3 exercises 4 problems chapter 7. the zeta function and prime number the-orem 1 zeros of tile zeta function hl esthnates for 1/c(s) 2 reduction to the functions 2.1 proof of the asymptotics for note on interchanging double sums 3 exercises 4 problems chapter 8. conformal mappings chapter 9. an introduction to elliptic functions chapter 10. applications of theta functions appendix a: asymptotics appendix b: simple connectivity and jordan curve theorem notes and references bibliography symbol glossary index |
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