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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalized Schwarz lemma at the boundary
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by Dov Chelst PDF
Proc. Amer. Math. Soc. 129 (2001), 3275-3278 Request permission

Abstract:

Let $\phi$ be an analytic function mapping the unit disc $\mathbb {D}$ to itself. We generalize a boundary version of Schwarz’s lemma proven by D. Burns and S. Krantz and provide sufficient conditions on the local behavior of $\phi$ near a finite set of boundary points that requires $\phi$ to be a finite Blaschke product. Afterwards, we supply several counterexamples to illustrate that these conditions may also be necessary.
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Additional Information
  • Dov Chelst
  • Affiliation: Department of Mathematics, Hill Center, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd., Piscataway, New Jersey 08854-8019
  • Email: chelst@math.rutgers.edu
  • Received by editor(s): March 10, 2000
  • Published electronically: June 6, 2001
  • Additional Notes: The author would like to thank Dr. R.B. Burckel for referring him to the article by Krantz and Burns and to also thank Drs. X. Huang, S. Goldstein and B. Walsh for their advice on this article’s contents.
  • Communicated by: Juha M. Heinonen
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3275-3278
  • MSC (2000): Primary 30C80
  • DOI: https://doi.org/10.1090/S0002-9939-01-06144-5
  • MathSciNet review: 1845002