A Schwarz lemma on the polydisk
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- by Greg Knese PDF
- Proc. Amer. Math. Soc. 135 (2007), 2759-2768 Request permission
Abstract:
We prove a generalization of the infinitesimal portion of the classical Schwarz lemma for functions from the polydisk to the disk. In particular, we describe the functions which play the role of automorphisms of the disk in this context–they turn out to be rational inner functions in the Schur-Agler class of the polydisk with an added symmetry constraint. In addition, some sufficient conditions are given for a function to be of this type.References
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- John P. D’Angelo, Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993. MR 1224231
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
Additional Information
- Greg Knese
- Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130
- MR Author ID: 813491
- Email: geknese@math.wustl.edu
- Received by editor(s): April 10, 2006
- Received by editor(s) in revised form: May 1, 2006
- Published electronically: March 30, 2007
- Additional Notes: Thanks to John McCarthy for his advice at all stages of this research.
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2759-2768
- MSC (2000): Primary 30C80; Secondary 32A30, 47A57
- DOI: https://doi.org/10.1090/S0002-9939-07-08766-7
- MathSciNet review: 2317950