Arkiv för Matematik

  • Ark. Mat.
  • Volume 30, Number 1-2 (1992), 61-81.

Extremal mappings for the Schwarz lemma

Seán Dineen and Richard M. Timoney

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Ark. Mat., Volume 30, Number 1-2 (1992), 61-81.

Received: 5 June 1990
First available in Project Euclid: 31 January 2017

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1992 © Institut Mittag-Leffler


Dineen, Seán; Timoney, Richard M. Extremal mappings for the Schwarz lemma. Ark. Mat. 30 (1992), no. 1-2, 61--81. doi:10.1007/BF02384862.

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  • Alexander, H., Extremal holomorphic embeddings between the ball and polydisc, Proc. Amer. Math. Soc. (2)68 (1978), 200–202.
  • Barth, T. J., The Kobayashi indicatrix at the center of a circular domain, Proc. Amer. Math. Soc. 88 (1983), 527–530.
  • Carathéodory, C., Über die Abbildungen, die durch Systeme von analytischen Funktionen von meheren Veränderlichen erzeugt werden, Math. Z. 34 (1932), 758–792.
  • Cartan, H., Sur les fonctions de plusieurs variables complexes. L'itération des transformations intérieurs d'un domaine borné, Math. Z. 35 (1932), 760–773.
  • Dineen, S., The Schwarz Lemma, Oxford Mathematical Monographs, Oxford, 1989.
  • Dineen, S. and Timoney, R. M., The algebraic metric of Harris on JB*-triple systems, Proc. Roy. Irish Acad. 90A (1990), 83–97.
  • Fornaess, J. E. and Stout, E. L., Polydiscs in complex imanifolds, Math. Ann. 227 (1977), 145–153.
  • Harris, L., Schwarz's lemma and the maximum primciple in infinite dimensional spaces, Ph.D. thesis, Cornell University, 1969.
  • John, F., Extremum problems with inequalities as side conditions, in R. Courant Anniversary Volume, Interscience, New York, 1948, pp. 187–204.
  • Kubota, Y., An extremal problem on the classical Cartan domains, Kodai Math. J. 4 (1981), 278–287.
  • Kubota, Y., A note on holomorphic imbeddings of the classical Cartan domains into the unit ball, Proc. Amer. Math. Soc. 85 (1982), 65–68.
  • Kubota, Y., An extremal problem on bounded symmetric domains, Bull. London Math. Soc. 15 (1983), 126–130.
  • Lempert, L., A note on mapping polydiscs into balls and vice versa, Acta Math. Acad. Sci. Hungar. 34 (1979), 117–119.
  • Lewis, D. R., Ellipsoids defined by Banach ideal norms, Mathematika 26 (1979), 18–29.
  • Mujica, J., Complex Analysis in Banach Spaces, Mathematical Studies 120, North-Holland, Amsterdam, 1986.
  • Pełczynski, A., Geometry of finite dimensional Banach spaces and operator ideals, in Notes in Banach Spaces (H.E. Lacey, editor), University of Texas Press, Austin, 1980, pp. 81–181.
  • Sadullaev, A., Schwarz lemma for circular domains and its applications, Math. Notes 27 (1980), 120–125.
  • Travaglini, G., An analogue of the Schwarz lemma for bounded symmetric domains, Proc. Amer. Math. Soc. 88 (1983), 85–88.