作者：(美)贝莱恩斯坦
页数：650
出版社：世界图书出版公司
出版日期：2012
ISBN：9787510040658
电子书格式：pdf/epub/txt
内容简介
贝莱恩斯坦编著的《复变导论（英文影印版）》给出了一个全纯函数性质的概述。内容全面，囊括了微分形式、同伦理论、同调理论和全纯函数的解析性质、非同质的Cauchy-Riemann方程的可解性和子调和函数理论，引入层理论、覆盖空间和黎曼曲面。为了帮助读者更好地理解书中的材料，增加了大量不同难度的习题。
目录
prefacechapter 1 topology of the complex plane and holomorphicfunctions1.1. some linear algebra and differential calculus1.2. differential forms on an open subset fl of c1.3. partitions of unity1.4. regular boundaries1.5. integration of differential forms of degree 2. the stokesformula1.6. homotopy. fundamental group1.7. integration of closed i-forms along continuous paths1.8. index of a loop1.9. homology1.10. residues1.11. holomorphic functionschapter 2 analytic properties of holomorphic functions2.1. integral representation formulas2.2. the frechet space2.3. holomorphic maps2.4. isolated singularities and residues2.5. residues and the computation of definite integrals2.6. other applications of the residue theorem2.7. the area theorem2.8. conformal mappingschapter 3 the -equation3.1. runge’stheorem3.2. mittag-leffier’s theorem3.3. the weierstrass theorem3.4. an interpolation theorem3.5. closed ideals in (ω)3.6. the operator σ acting on distributions3.7. mergelyan’s theorem3.8. short survey of the theory of distributions. their relation tothetheory of residueschapter 4 harmonic and subharmonic functions4.1. introduction4.2. a remark on the theory of integration4.3. harmonic functions4.4. subharmonic functions4.5. order and type of subharmonic functions in c4.6. integral representations4.7. green functions and harmonic measure4.8. smoothness up to the boundary of biholomorphic mappings4.9. introduction to potential theorychapter 5 analytic continuation and singularities5.1. introduction5.2. elementary study of singularities and dirichlet series5.3. a brief study of the functions f and5.4. covering spaces5.5. riemann surfaces5.6. the sheaf of germs of holomorphic functions5.7. cocycles5.8. group actions and covering spaces5.9. galois coverings5.10 the exact sequence of a galois covering5.11. universal covering space5.12. algebraic functions, i5.13. algebraic functions, ii5.14. the periods of a differential form5.15. linear differential equations5.16. the index of differential operatorsreferencesnotation and selected terminologyindex
