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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A constructive Schwarz reflection principle


Author: Jeremy Clark
Journal: Trans. Amer. Math. Soc. 355 (2003), 4569-4579
MSC (2000): Primary 03F60, 30E99
Published electronically: July 8, 2003
MathSciNet review: 1990762
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Abstract: We prove a constructive version of the Schwarz reflection principle. Our proof techniques are in line with Bishop's development of constructive analysis. The principle we prove enables us to reflect analytic functions in the real line, given that the imaginary part of the function converges to zero near the real line in a uniform fashion. This form of convergence to zero is classically equivalent to pointwise convergence, but may be a stronger condition from the constructivist point of view.


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Additional Information

Jeremy Clark
Affiliation: 107 Rue de Sèvres, Paris 75006, France
Email: jclark@noos.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03359-2
PII: S 0002-9947(03)03359-2
Received by editor(s): November 5, 2002
Received by editor(s) in revised form: November 11, 2002
Published electronically: July 8, 2003
Article copyright: © Copyright 2003 American Mathematical Society