Classical Topics in Complex Function Theory, Volume 172

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Springer, 1998 - Mathematics - 349 pages
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An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike
  

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Contents

V
3
VI
4
VII
6
VIII
7
X
9
XI
10
XII
12
XIV
14
CLVIII
171
CLIX
172
CLX
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CLXI
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CLXIII
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CLXV
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CLXVI
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CLXVII
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XV
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XVI
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XVIII
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XIX
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XXXI
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XXXIX
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XLI
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XCI
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XCV
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XCIX
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C
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CI
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CII
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CVIII
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CIX
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CXI
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CXII
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CXIV
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CXV
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CXIX
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CXX
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CXXI
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CXL
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CXLI
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CXLIII
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CXLV
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CXLIX
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CL
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CLI
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CLII
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CLIII
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CLIV
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CLVI
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CLVII
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CLXVIII
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CLXX
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CLXXI
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CLXXIII
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CLXXIV
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CLXXV
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CLXXVII
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CLXXIX
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CLXXXII
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CLXXXIII
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CLXXXIV
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CXC
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CXCI
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CXCVI
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CC
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CCI
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CCII
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CCVII
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CCXI
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CCXII
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CCXIV
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CCXVI
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CCXVII
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CCXVIII
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CCXX
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CCXXI
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CCXXII
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CCXXIII
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CCXXIV
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CCXXVI
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CCXXVII
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CCXXVIII
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CCXXIX
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CCXXX
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CCXXXI
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CCXXXII
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CCXXXV
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CCXXXVI
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CCXXXVII
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CCXXXIX
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CCXL
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CCXLI
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CCXLII
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CCXLV
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CCXLVI
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CCXLVII
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CCXLVIII
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CCXLIX
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CCLI
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CCLII
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CCLIII
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CCLIV
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CCLVI
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CCLVIII
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CCLIX
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CCLXI
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CCLXII
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CCLXIII
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CCLXIV
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CCLXV
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CCLXVI
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CCLXVII
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CCLXVIII
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CCLXX
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CCLXXI
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CCLXXII
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CCLXXIV
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CCLXXV
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CCLXXVI
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CCLXXVII
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CCLXXIX
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CCLXXX
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CCLXXXI
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CCLXXXII
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CCLXXXIV
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CCLXXXV
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CCLXXXVI
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CCLXXXVIII
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CCLXXXIX
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CCXC
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CCXCI
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CCXCII
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CCXCIV
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CCXCV
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CCXCVII
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CCXCVIII
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CCC
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CCCI
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CCCII
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CCCIII
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CCCIV
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CCCV
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CCCVII
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CCCVIII
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CCCIX
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CCCX
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CCCXII
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CCCXIII
329
CCCXIV
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CCCXV
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About the author (1998)

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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