Graduate Texts in Mathematics: Classical Topics in Complex Function Theory (Hardback)

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VERY GOOD: This book is in very good condition, showing slight wear on the cover corners. The pages are free of writing and were printed on acid-free paper. The binding is tight, as if the book has never been opened (LIKE NEW).

Product Details

This is Volume 172 in Springer'sGraduate Texts in Mathematics series.

Continued from the back cover: "The book contains numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. Topics covered include Weierstrass's product theorem, Mittag-Leffler's theorem, the Riemann mapping theorem, and Runge's theorems on approximation of analytic functions. In addition to these standard topics, the reader will find Eisenstein's proof of Euler's product formula for the sine function; Weilandt's uniqueness theorem for the gamma function and applications; a detailed discussion of Stirling's formula; Iss'sa's theorem; Besse's proof that all domains in C are domains of holomorphy; Wedderburn's lemma and the ideal theory of rings of holomorphic functions; Estermann's proofs of the overconvergence theorem and Block's theorem; a holomorphic imbedding of the unit disc in C³; and Gauss's expert opinion of November 1851 on Riemann's 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, will make this book an invaluable source for students and teachers."

BRIEF CONTENTS

A. Infinite Products and Partial Fraction Series

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

B. Mapping Theory

7. The Theorems of Montel and Vitali
8. The Riemann Mapping Theorem
9. Automorphisms and Finite Inner Maps

C. Selecta

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

Each chapter has multiple sections, and these in turn have bibliographies. The end of the text consists of Short Biographies, Symbol Index, Name Index, and Subject Index.