Theory of Complex Functions

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Springer New York, Feb 1, 1999 - Mathematics - 458 pages
Wohl dem, der seiner Viiter gem gedenkt (Blessings on him who gladly remembers his forefathers) - J. W. v. GOETHE 1. . . . "Zuvorderst wiirde ich jemand, der eine neue Function in die Analyse einfiihren will, urn eine Erklarung bitten, ob er sie schlechterdings bloss auf reelle Grossen (reelle Werthe des Arguments der Function) angewandt wis sen will, und die imaginaren Wert he des Arguments gleichsam nur als ein Uberbein ansieht - oder ob er meinem Grundsatz beitrete, dass man in dem Reiche der Grossen die imaginaren a + byCI = a + bi als gleiche Rechte mit den reellen geniessend ansehen miisse. Es ist hier nicht von prakti schem Nutzen die Rede, sondern die Analyse ist mir eine selbstandige Wis senschaft, die durch Zuriicksetzung jener fingirten Grossen ausserordentlich an Schonheit und Rundung verlieren und alle Augenblick Wahrheiten, die sonst allgemein gelten, hochst liiBtige Beschrankungen beizufiigen genothigt sein wiirde . . . (At the very beginning I would ask anyone who wants to introduce a new function into analysis to clarify whether he intends to confine it to real magnitudes (real values of its argument) and regard the imaginary values as just vestigial - or whether he subscribes to my fun damental proposition that in the realm of magnitudes the imaginary ones a + byCI = a + bi have to be regarded as enjoying equal rights with the real ones. We are not talking about practical utility here; rather analy sis is, to my mind, a self-sufficient science.

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About the author (1999)

Hans Grauert (b. 1930 in Harem /Ems, Germany) and Reinhold Remmert (b. 1930 in OsnabrA1/4ck, Germany) met at the University of MA1/4nster, where they both studied mathematics and physics from 1949 to 1954. In 1950 they were invited by Heinrich Behnke and Karl Stein to attend their "Oberseminar," which was held on Saturdays, for 2 hours from 9 a.m.

Five years after the tragic events of World War 2, Behnke's old friend Henri Cartan visited MA1/4nster. His lecture on recent developments in the theory of "Several Complex Variables" was a real eye-opener for the young students and had a strongly formative influence on them: indeed this was to determine the course of their scientific research careers from then on.

In June 1954 Grauert and Remmert received their respective doctorates from the University of MA1/4nster. In 1957 they both became lecturer (Privatdozent) there. In 1959 resp. 1960, Grauert and Remmert were appointed full professors at GAttingen resp. Erlangen.

The original German edition of "Theory of Stein Spaces" was written at a time when complex spaces, coherent analytic sheaves and the so-called Theorems A and B had already become established notions and theorems. Dedicated to Karl Stein, the book was published in 1977, and the English edition was to follow in 1979. The first announcement of the book, in Springer's promotion, consisted of the picture reproduced on the inside cover flap of this book, taken during the boat trip of the annual Bonn Arbeitstagung some time earlier, showing three men on a boat, with the minimalistic caption "Grundlehren 227.

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