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Generalized Schwarzian derivatives for generalized fractional linear transformations

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EN
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.
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  • Department of Pure Mathematics, University of Sydney, Sydney, New South Wales 2006, Australia
Bibliografia
  • [1] L. V. Ahlfors, Clifford numbers and Möbius transformations in $ℝ^n$, in: Clifford Algebras and their Applications in Mathematical Phisics, J. S. R. Chrisholm and A. K. Common (eds.), NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., Vol. 183, Reidel, 1986, 167-175.
  • [2] L. V. Ahlfors, Möbius transformations in $ℝ^n$ expressed through 2 × 2 matrices of Clifford numbers, Complex Variables 5 (1986), 215-224.
  • [3] L. V. Ahlfors, Cross-ratios and Schwarzian derivatives in $ℝ^n$, preprint.
  • [4] M. F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38.
  • [5] K. Carne, The Schwarzian derivative for conformal maps, to appear.
  • [6] J. Elstrodt, F. Grunewald and J. Mennicke, Vahlen's group of Clifford matrices and Spin-groups, Math. Z. 196 (1987), 369-390.
  • [7] K. Gross and R. Kunze, Bessel functions and representation theory, II. Holomorphic discrete series and metaplectic representations, J. Funct. Anal. 25 (1977), 1-49.
  • [8] H. P. Jakobsen, Intertwining differential operators for Mp(n,ℝ) and U(n,n), Trans. Amer. Math. Soc. 246 (1978), 311-337.
  • [9] H. P. Jakobsen and M. Vergne, Wave and Dirac operators and representations of the conformal group, J. Funct. Anal. 24 (1977), 52-106.
  • [10] O. Lehto, Univalent Functions and Teichmüller Spaces, Graduate Texts in Math. 109, Springer, 1986.
  • [11] H. Maass, Automorphe Funktionen von mehreren Veränderlichen und Dirichletsche Reihen, Abh. Math. Sem. Univ. Hamburg 16 (1949), 72-100.
  • [12] P. Osgood and D. Stowe, The Schwarzian derivative and conformal mapping of Riemannian manifolds, to appear.
  • [13] P. Osgood and D. Stowe, A generalization of Nehari's univalence criterion, to appear.
  • [14] I. R. Porteous, Topological Geometry, Cambridge Univ. Press, 1981.
  • [15] K. Th. Vahlen, Ueber Bewegungen und complexe Zahlen, Math. Ann. 55 (1902), 585-593.
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bwmeta1.element.bwnjournal-article-apmv57z1p29bwm
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