## Function Theory of Several Complex VariablesKrantz has a very readable style and this is one math book that is fun reading (assuming you have the background listed above). No definition causes you to wonder why it was defined, and no theorem causes you to wonder why it was proved. It's also one of the few books that defines sheaf cohomology in terms of actual geometric intuition and concrete examples. Even readers not interested in several complex variables should benefit from the way he treats tangential subjects in this book. |

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### Contents

An Introduction to the Subject | 1 |

Some Integral Formulas | 13 |

Subharmonicity and Its Applications | 69 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

analytic Apply assume ball Bergman biholomorphic boundary bounded called Chapter Choose closed coefficients compact complex compute Conclude condition consider constant construct contains continuous converges convex coordinates Corollary Cousin covering Define defining function definition denote differential dimension disc domain of holomorphy element equation equivalent estimates example exists extends fact Figure Finally fixed follows formula given gives harmonic Hartogs holds holomorphic functions implies integral kernel Lemma Let f Let S CC Levi manifold Math measure metric Miscellaneous Exercise neighborhood normal Note Notice obtain open set operator Peas plush polynomial problem Proof Proof Let PROPOSITION prove pseudoconvex domains Reader Remark result satisfies sense sequence sheaf smooth solution solved space strongly pseudoconvex subharmonic sufficiently supported Suppose theorem theory trivial unit variable write zero