From the reviews of the first printing, published as Volume 7 of the Encyclopaedia of Mathematical Sciences: "...... In this volume, we find an introductory essay entitled "Remarkable Facts of Complex Analysis" by Vitushkin... This is followed by articles by G.M.Khenkin on integral formulas in complex analysis, by E.M.Chirka on complex analytic sets, by Vitushkin on the geometry of hypersurfaces and by P.Dolbeault, on the theory of residues in several variables. ... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; all contain substantial lists of references." Bulletin of the American Mathematical Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift fรผr Angewandte Mathematik und Physik 1990 "... comprehensive and authoritative survey of results in contemporary mathematics, indications of the directions of its future development, the material presented around pivotal facts whose understanding enables one to have a general view of the area, no proofs or only the outline of proofs, and extensive bibliographies. ... Browsing through this collection of surveys gives one a feeling of awe and admiration. Truly, complex analysis is vigorously alive. ... They are highly recommended to everyone with an interest in complex analysis." Medelingen van het wiskundig genootshap, 1992
CONTENT
I. Remarkable Facts of Complex Analysis -- II. The Method of Integral Representations in Complex Analysis -- III. Complex Analytic Sets -- IV. Holomorphic Mappings and the Geometry of Hypersurfaces -- V. General Theory of Multidimensional Residues -- Author Index
