ENGLISH

The Basic theory of power series

By Jesus M. Ruiz

Book information

Publisher
Vieweg
Year
1993
ISBN
3528065257, 9783528065256
ISSN
0932-7134
LCC
QA251.3 .R85 1993
Language
english
Format
DJVU
Filesize
921 kB (943542 bytes)
Series
Advanced lectures in mathematics
Pages
144\144
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2009-07-20 03:45:11

Description

This volume covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any branches of mathematics, particularly in complex and in real analytic geometry, in commutative algebra, in algebraic geometry and in real algebraic geometry. In particular it presents Rueckert's complex nullstellensatz, Risler's real nullstellensatz, Tougeron's implicit function theorem and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. This had the advantage that he sees many theorems about power series as special instances of more general facts, but on the other hand made it highly time consuming to understand all these theorems. The present book opens another path - one gets acquainted with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, as well as some others.

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