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Zbl 0685.32001
Hörmander, Lars
An introduction to complex analysis in several variables. 3rd revised ed. (English)
[B] North-Holland Mathematical Library, 7. Amsterdam etc.: North-Holland. xii, 254 p. {\$}71.75; Dfl. 140.00 (1990). ISBN 0-444-88446-7

The author's book [1st ed. (1966; Zbl 0138.062), 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. \par 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.
[G.Ehrig]

MSC 2000:: *32-02 Research monographs (several complex variables)
32U05 Plurisubharmonic functions and generalizations
32D15 Continuation of analytic objects (several variables)
32E05 Holomorphically convex complex spaces
32E20 Polynomial convexity
32E10 Stein spaces and manifolds
32W05 $\overline\partial$ and $\overline\partial$-Neumann operators
32B05 Analytic algebras and generalizations

Keywords: complex analysis in several variables; ${\bar \partial }$ Neumann problem

Citations: Zbl 0138.062; Zbl 0271.32001

Cited in: Zbl 1043.35123 Zbl 0835.32001 Zbl 0770.32008

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