A characterization of linear automorphisms of the Euclidean ball

Hidetaka Hamada; Tatsuhiro Honda

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 1, page 79-85
  • ISSN: 0066-2216

Abstract

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Let B be the open unit ball for a norm on ℂ n . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on ℂ n . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

How to cite

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Hamada, Hidetaka, and Honda, Tatsuhiro. "A characterization of linear automorphisms of the Euclidean ball." Annales Polonici Mathematici 72.1 (1999): 79-85. <http://eudml.org/doc/262853>.

@article{Hamada1999,
abstract = {Let B be the open unit ball for a norm on $ℂ^n$. Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on $ℂ^n$. Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.},
author = {Hamada, Hidetaka, Honda, Tatsuhiro},
journal = {Annales Polonici Mathematici},
keywords = {automorphism; complex extreme point; totally real; non-pluripolar; Schwarz lemma; complex extreme points},
language = {eng},
number = {1},
pages = {79-85},
title = {A characterization of linear automorphisms of the Euclidean ball},
url = {http://eudml.org/doc/262853},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Hamada, Hidetaka
AU - Honda, Tatsuhiro
TI - A characterization of linear automorphisms of the Euclidean ball
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 1
SP - 79
EP - 85
AB - Let B be the open unit ball for a norm on $ℂ^n$. Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on $ℂ^n$. Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.
LA - eng
KW - automorphism; complex extreme point; totally real; non-pluripolar; Schwarz lemma; complex extreme points
UR - http://eudml.org/doc/262853
ER -

References

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  2. [2] T. J. Barth, The Kobayashi indicatrix at the center of a circular domain, Proc. Amer. Math. Soc. 88 (1983), 527-530. Zbl0494.32008
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  4. [4] H. Hamada, A Schwarz lemma in several complex variables, in: Proc. Third Internat. Colloq. on Finite or Infinite Dimensional Complex Analysis, Seoul, Korea, 1995, 105-110. 
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  7. [7] T. Honda, A special version of the Schwarz lemma on an infinite dimensional domain, Rend. Mat. Accad. Lincei 9 (1997), 107-110. Zbl0890.32012
  8. [8] T. Honda, Linear isometries on Hilbert spaces, Complex Variables, to appear. 
  9. [9] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter, Berlin, 1993. Zbl0789.32001
  10. [10] K. H. Shon, On Riemann domains containing a certain real domain, Complex Variables 31 (1996), 27-35. Zbl0865.32010
  11. [11] E. Vesentini, Variations on a theme of Carathéodory, Ann. Scuola Norm. Sup. Pisa 7 (1979), 39-68. Zbl0413.46039
  12. [12] E. Vesentini, Complex geodesics, Compositio Math. 44 (1981), 375-394. Zbl0488.30015
  13. [13] J. P. Vigué, Un lemme de Schwarz pour les domaines bornés symétriques irréductibles et certains domaines bornés strictement convexes, Indiana Univ. Math. J. 40 (1991), 239-304. Zbl0733.32025
  14. [14] J. P. Vigué, Le lemme de Schwarz et la caractérisation des automorphismes analytiques, Astérisque 217 (1993), 241-249. 

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