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**An introduction to complex analysis in several variables.
3rd revised ed.**
*(English)*
Zbl 0685.32001

North-Holland Mathematical Library, 7. Amsterdam etc.: North-Holland. xii, 254 p. $71.75; Dfl. 140.00 (1990).

The author’s book [1st ed. (1966; Zbl 0138.06203), 2nd. ed. (1973; Zbl 0271.32001)] is known to deal with topics in complex analysis in several variables based on the theory of partial differential equations, more exactly on the solution of the \(\bar\partial\) Neumann problem as the main tool. In this third edition several additions are made where these methods are particularly important: The new section 7.7 is devoted to the study of modules with polynomial generators in order to prove the full “fundamental principle” of Ehrenpreis. For this reason the earlier section 7.6 on “Cohomology on bounds” is modified.

A new section 6.5 on analytic sets is added. Finally, a discussion of the theorem of Siu on Lelong numbers of plurisubharmonic functions is included.

A new section 6.5 on analytic sets is added. Finally, a discussion of the theorem of Siu on Lelong numbers of plurisubharmonic functions is included.

Reviewer: Gertraud Ehrig (Berlin)

### MSC:

32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |

32U05 | Plurisubharmonic functions and generalizations |

32D15 | Continuation of analytic objects in several complex variables |

32E05 | Holomorphically convex complex spaces, reduction theory |

32E20 | Polynomial convexity, rational convexity, meromorphic convexity in several complex variables |

32E10 | Stein spaces |

32W05 | \(\overline\partial\) and \(\overline\partial\)-Neumann operators |

32B05 | Analytic algebras and generalizations, preparation theorems |