# Generalized Schwarzian derivatives for generalized fractional linear transformations

Annales Polonici Mathematici (1992)

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

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topJohn 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] L. V. Ahlfors, Möbius transformations in ${\mathbb{R}}^{n}$ expressed through 2 × 2 matrices of Clifford numbers, Complex Variables 5 (1986), 215-224.
- [3] L. V. Ahlfors, Cross-ratios and Schwarzian derivatives in ${\mathbb{R}}^{n}$, preprint.
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- [5] K. Carne, The Schwarzian derivative for conformal maps, to appear. Zbl0705.30010
- [6] J. Elstrodt, F. Grunewald and J. Mennicke, Vahlen's group of Clifford matrices and Spin-groups, Math. Z. 196 (1987), 369-390. Zbl0611.20027
- [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. Zbl0361.22007
- [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. Zbl0361.22012
- [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. Zbl0034.34801
- [12] P. Osgood and D. Stowe, The Schwarzian derivative and conformal mapping of Riemannian manifolds, to appear. Zbl0766.53034
- [13] P. Osgood and D. Stowe, A generalization of Nehari's univalence criterion, to appear. Zbl0722.53029
- [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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