## Lectures on functions of several complex variables |

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### Contents

Elementary properties of functions of several complex variables | 29 |

Applications to commutative Banach algebras | 80 |

L estimates and existence theorems for the 3 operator | 100 |

4 other sections not shown

### Common terms and phrases

A(fi A(SI analytic function arbitrary assume boundary coefficients coherent analytic sheaf cohomology compact set compact subset completes the proof complex manifold component condition contained continuous function converges coordinate system Corollary Cousin problem cp(z defined definition denote differential disc domain of holomorphy elements equation equivalent f e A(ft finite number follows from Theorem forms of type function f functions in A(ft gives Hence ideal implies integral interior isomorphic Lemma Let ft linear manifold ft meromorphic function neighborhood obtain open set open set ft open subset plurisubharmonic function polydisc proof of Theorem proves the theorem pseudoconvex Reinhardt domain relatively compact Runge domain satisfies sequence space Stein manifold strictly plurisubharmonic subharmonic subset of ft sup f topology u e A(ft uniformly vanish Weierstrass polynomial z e ft