Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. Errett Bishop and Douglas Bridges, Constructive Analysis, Grundlehren der Math. Wissenschaften 279, Springer-Verlag, Heidelberg-Berlin-New York, 1985. MR 87d:03172
  • 2. Douglas Bridges and Fred Richman, Varieties of Constructive Mathematics, London Mathematical Society Lecture Note Series 97, Cambridge University Press, Cambridge-New York-Melbourne, 1987. MR 88k:03127
  • 3. Theodore W. Gamelin, Complex Analysis, Undergraduate Texts in Mathematics, Springer-Verlag, Heidelberg-Berlin-New York, 2001. MR 2002h:30001

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03F60, 30E99

Retrieve articles in all journals with MSC (2000): 03F60, 30E99

Additional Information

Jeremy Clark
Affiliation: 107 Rue de Sèvres, Paris 75006, France

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