Generalized Schwarzian derivatives for generalized fractional linear transformations

John Ryan

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 1, page 29-44
  • ISSN: 0066-2216

Abstract

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Generalizations of the classical Schwarzian derivative of complex analysis have been proposed by Osgood and Stowe [12, 13], Carne [5], and Ahlfors [3]. We present another generalization of the Schwarzian derivative over vector spaces.

How to cite

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John Ryan. "Generalized Schwarzian derivatives for generalized fractional linear transformations." Annales Polonici Mathematici 57.1 (1992): 29-44. <http://eudml.org/doc/262343>.

@article{JohnRyan1992,
abstract = {Generalizations of the classical Schwarzian derivative of complex analysis have been proposed by Osgood and Stowe [12, 13], Carne [5], and Ahlfors [3]. We present another generalization of the Schwarzian derivative over vector spaces.},
author = {John Ryan},
journal = {Annales Polonici Mathematici},
keywords = {Clifford functions; Schwarzian derivative; Clifford algebra; local diffeomorphisms},
language = {eng},
number = {1},
pages = {29-44},
title = {Generalized Schwarzian derivatives for generalized fractional linear transformations},
url = {http://eudml.org/doc/262343},
volume = {57},
year = {1992},
}

TY - JOUR
AU - John Ryan
TI - Generalized Schwarzian derivatives for generalized fractional linear transformations
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 1
SP - 29
EP - 44
AB - Generalizations of the classical Schwarzian derivative of complex analysis have been proposed by Osgood and Stowe [12, 13], Carne [5], and Ahlfors [3]. We present another generalization of the Schwarzian derivative over vector spaces.
LA - eng
KW - Clifford functions; Schwarzian derivative; Clifford algebra; local diffeomorphisms
UR - http://eudml.org/doc/262343
ER -

References

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  2. [2] L. V. Ahlfors, Möbius transformations in ℝ n expressed through 2 × 2 matrices of Clifford numbers, Complex Variables 5 (1986), 215-224. 
  3. [3] L. V. Ahlfors, Cross-ratios and Schwarzian derivatives in ℝ n , preprint. 
  4. [4] M. F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38. 
  5. [5] K. Carne, The Schwarzian derivative for conformal maps, to appear. Zbl0705.30010
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  9. [9] H. P. Jakobsen and M. Vergne, Wave and Dirac operators and representations of the conformal group, J. Funct. Anal. 24 (1977), 52-106. Zbl0361.22012
  10. [10] O. Lehto, Univalent Functions and Teichmüller Spaces, Graduate Texts in Math. 109, Springer, 1986. 
  11. [11] H. Maass, Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Univ. Hamburg 16 (1949), 72-100. Zbl0034.34801
  12. [12] P. Osgood and D. Stowe, The Schwarzian derivative and conformal mapping of Riemannian manifolds, to appear. Zbl0766.53034
  13. [13] P. Osgood and D. Stowe, A generalization of Nehari's univalence criterion, to appear. Zbl0722.53029
  14. [14] I. R. Porteous, Topological Geometry, Cambridge Univ. Press, 1981. 
  15. [15] K. Th. Vahlen, Ueber Bewegungen und complexe Zahlen, Math. Ann. 55 (1902), 585-593. 

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