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.


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