Function Theory of Several Complex Variables 2E - Krantz, Steven

Function Theory of Several Complex Variables 2E

Steven Krantz

Yayınevi: American Mathematical Society AMS

Yayın tarihi: 08/2004

ISBN: 9780821827246

Ciltli | İngilizce | 564 Sayfa |

Tür: Matematik-İstatistik

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Description

This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.

Table of Contents

Preface to the Second Edition
Preface to the First Edition
An Introduction to the Subject 1
1 Some Integral Formulas 19
1.1 The Bochner-Martinelli Formula 19
1.2 Applications of Cauchy Theory and the [actual symbol not reproducible] Equation 31
1.3 Basic Properties of Harmonic Functions 35
1.4 The Bergman Kernel 49
1.5 The Szego and Poisson-Szego Kernels 66
1.6 Afterword to Chapter 1 69
2 Subharmonicity and Its Applications 81
2.1 Subharmonic Functions 81
2.2 Pluriharmonic and Plurisubharmonic Functions 94
2.3 Power Series 99
2.4 Hartogs's Theorem on Separate Analyticity 107
3 Convexity 117
3.1 Many Notions of Convexity 117
3.2 Convexity and Pseudoconvexity 132
3.3 Pseudoconvexity, Plurisubharmonicity, and Analytic Discs 142
3.4 Domains of Holomorphy 151
3.5 Examples of Domains of Holomorphy and the Edge-of-the-Wedge Theorem 159
4 Hormander's Solution of the [actual symbol not reproducible] Equation 175
4.1 Generalities about the [actual symbol not reproducible] Problem 175
4.2 Unbounded Operators on a Hilbert Space 176
4.3 The Formalism of the [actual symbol not reproducible] Problem 179
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