zbMATH — the first resource for mathematics

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.
Reviewer: J.Lorenz

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)