Introduction to Complex Analysis (v. 1) (Encyclopaedia of Mathematical Sciences) - Hardcover

Hardcover

ISBN 10: 3540170049 ISBN 13: 9783540170044

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1989

Synopsis

This volume consists of 5 contributions. The first one presents a brief discussion of some important facts of complex analysis. The other contributions give extended surveys in integral representation theory, complex analytic sets, holomorphic mappings and geometry of surfaces, and multidimensional residue theory. Complete information on modern methods and results in complex analysis is given.

About this title

Review

From the reviews: "... 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; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.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 für Angewandte Mathematik und Physik, 199

From the Back Cover

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 für 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

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1989
• ISBN 10: 3540170049
• ISBN 13: 9783540170044
• Binding: Hardcover
• Language: English
• Number of pages: 255
• Editor: Vitrushkin A.G.