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Remarks on the Analytic Implicit Function Theorem

✍ Scribed by Erich Berger

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
331 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper, we focus attention on the problem of to what extent abstract Banach space concepts can be utilized in order to simplify well-known formulas for the power series expansion of an implicitly defined holomorphic mapping in the Ž finite-dimensional case. The formulas obtained in the previous literature roughly . speaking, extensions of the Burmann᎐Lagrange formula are extremely lengthy Ànd involved. Our main purpose here is to give a more condensed and more comprehensible version of such a formula. The basic idea of the proof consists in combining the technique of multiple residues with certain elementary concepts Ž . multilinear algebra from differential calculus in Banach spaces.

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