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Volume 4, Issue 1, Article 12 |
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The Analytic Domain in the Implicit Function Theorem
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Authors: |
H.C. Chang, W. He, N. Prabhu, |
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Keywords:
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Implicit Function Theorem, Analytic Functions. |
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Date Received:
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30/05/02 |
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Date Accepted:
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12/09/02 |
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Subject Codes: |
30E10
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Editors: |
Hari M. Srivastava, |
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Abstract: |
The Implicit Function Theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of analytic equations, as analytic functions of the remaining variables. We derive a nontrivial lower bound on the radius of such a ball. To the best of our knowledge, our result is the first bound on the domain of validity of the Implicit Function Theorem.
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