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

Hörmander, Lars

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.

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

Keywords:

complex analysis in several variables; \({\bar \partial }\) Neumann problem

Citations:

Zbl 0138.06203; Zbl 0271.32001