Analysis on real and complex manifolds. (3rd printing). (English) Zbl 0583.58001

Narasimhan, R.

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

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)

Keywords:

linear elliptic differential operators on manifolds