CHAPTER Ⅰ. ANALYTIC FUNCTIONS OF ONE COMPLEX VARIABLE
Summary
1.2. Preliminaries
1.2. Cauchy's integral formula and its applications
1.3. The Runge approximation theorem
1.4. The Mittag-Leffler theorem
1.5. The Weierstrass theorem
1.6. Subharmonic functions
Notes
CHAPTER Ⅱ. ELEMENTARY PROPERTIES OF FUNCTIONS OF SEVERAL COMPLEX VARIABLES
Summary
2.1. Preliminaries
2.2. Applications of Cauchy's integral formula in polydiscs
2.3. The inhomogeneous Cauchy-Riemann equations in a polydisc
2.4. Power series and Reinhardt domains
2.5. Domains of holomorphy
2.6. Pseudoconvexity and plurisubharmonicity
2.7. Runge domains
Notes
CHAPTER Ⅲ. APPLICATIONS TO COMMUTATIVE BANACH ALGEBRAS
Summary
3.1. Preliminaries
3.2. Analytic functions of elements in a Banach algebra
Notes
CHAPTER Ⅳ. L2 ESTIMATES AND EXISTENCE THEOREMS FOR THE e OPERATOR
Summary
4.1. Preliminaries
4.2. Existence theorems in pseudoconvex domains
4.3. Approximation theorems
4.4. Existence theorems in L2 spaces
4.5. Analytic functionals
Notes
CHAPTER Ⅴ. STEIN MANIFOLDS
Summary
5.1. Definitions
5.2. L2 estimates and existence theorems for the e operator
5.3. Embedding of Stein manifolds.
5.4. Envelopes of holomorphy.
5.5. The Cousin problems on a Stein manifold
5.6. Existence and approximation theorems for sections of an analytic vector bundle
5.7. Almost complex manifolds
Notes
CHAPTER Ⅵ. LOCAL PROPERTIES OF ANALYTIC FUNCTIONS
Summary
6.1. The Weierstrass preparation theorem
6.2. Factorization in the ring ,4o of germs of analytic functions
6.3. Finitely generated ,4o-modules
6.4. The Oka theorem
6.5. Analytic sets
Notes
CHAPTER Ⅶ. COHERENT ANALYTIC SHEAVES ON STEIN MANIFOLDS
Summary
7.1. Definition of sheaves
7.2. Existence of global sections of a coherent analytic sheaf
7.3. Cohomology groups with values in a sheaf
7.4. The cohomology groups of a Stein manifold with coefficients in a coherent analytic sheaf
7.5. The de Rham theorem
7.6. Cohomology with bounds and constant coefficient difterential equations
7.7. Quotients of AK by submodules, and the Ehrenpreis fundamental principle
Notes
BIBLIOGRAPHY
INDEX
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