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Zbl 0591.32002
Range, R.Michael
Holomorphic functions and integral representations in several complex variables. (English)
[B] Graduate Texts in Mathematics, 108. New York etc.: Springer-Verlag. XIX, 386 p. DM 128.00 (1986).

The methods of integral representations have invaded successfully the theory of functions of several complex variables in the 1970's, originating principally with the work of G. M. Henkin. The book under review is a textbook which presents an as elementary as possible exposition of this theory and of its main applications. The main topics covered are: integral representations of Cauchy-Fantappiè type, Levi problem and solution of ${\bar \partial}$ on strictly pseudoconvex domains, integral representations of Henkin-Ramirez and estimates for the ${\bar \partial}$-problem, boundary regularity of biholomorphic maps. Historical comments and indications on recent developments are given.
[G.Roos]

MSC 2000:: *32A25 Integral representation of holomorphic functions (several variables)
32A10 Holomorphic functions (several variables)
32-01 Textbooks (several complex variables)
32T99 Pseudoconvex domains
32W05 $\overline\partial$ and $\overline\partial$-Neumann operators
32H99 Holomorphic mappings on analytic spaces

Keywords: holomorphic functions; integral representations of Cauchy-Fantappiè type; strictly pseudoconvex domains; ${\bar \partial }$-problem

Cited in: Zbl 1139.32001

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