Analysis on real and complex manifolds. (3rd printing).

*(English)*Zbl 0583.58001
North-Holland Mathematical Library, Vol. 35. Amsterdam - New York - Oxford: North-Holland. XIV, 246 p. $ 55.00; Dfl. 150.00 (1985).

This is a reprint of a book, which has become almost a classic and which has been out of print for a long time. The new edition contains an additional preface with general comments on the contents, some historical remarks on ”Poincaré’s lemma” (Poincaré had nothing to do with this result, it should be attributed to Volterra) and remarks on an alternative approach to the theory of linear elliptic differential operators on complex vector bundles, based on pseudodifferential operators with symbol from the class \(S^ m\), all with complete references (21 items).

Although its first printing appeared almost 20 years ago (1968; Zbl 0188.258) this book has remained up to date and modern. It constitutes an excellent text introducing global analysis.

Although its first printing appeared almost 20 years ago (1968; Zbl 0188.258) this book has remained up to date and modern. It constitutes an excellent text introducing global analysis.

Reviewer: J.Lorenz

##### MSC:

58-02 | Research exposition (monographs, survey articles) pertaining to global analysis |

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

58J40 | Pseudodifferential and Fourier integral operators on manifolds |

58A15 | Exterior differential systems (Cartan theory) |

58A17 | Pfaffian systems |

58A05 | Differentiable manifolds, foundations |

58A10 | Differential forms in global analysis |

37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |

37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |

58J32 | Boundary value problems on manifolds |

46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |

35J30 | Higher-order elliptic equations |

53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |

35D10 | Regularity of generalized solutions of PDE (MSC2000) |