Classical Topics in Complex Function Theory - Remmert, Reinhold

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Résumé :
1 Infinite Products of Holomorphic Functions.- 2 The Gamma Function.- 3 Entire Functions with Prescribed Zeros.- 4* Holomorphic Functions with Prescribed Zeros.- 5 Iss'sa's Theorem. Domains of Holomorphy.- 6 Functions with Prescribed Principal Parts.- 7 The Theorems of Montel and Vitali.- 8 The Riemann Mapping Theorem.- 9 Automorphisms and Finite Inner Maps.- 10 The Theorems of Bloch, Picard, and Schottky.- 11 Boundary Behavior of Power Series.- 12 Runge Theory for Compact Sets.- 13 Runge Theory for Regions.- 14 Invariance of the Number of Holes.- Short Biographies.- Symbol Index.- Name Index....

Sommaire:
Hans Grauert (b. 1930 in Harem /Ems, Germany) and Reinhold Remmert (b. 1930 in Osnabr?ck, Germany) met at the University of M?nster, 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 M?nster. 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 M?nster. In 1957 they both became lecturer (Privatdozent) there. In 1959 resp. 1960, Grauert and Remmert were appointed full professors at G?ttingen 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....