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1998 | 69 | 2 | 175-196
Tytuł artykułu

Effective formulas for invariant functions - case of elementary Reinhardt domains

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Słowa kluczowe
Rocznik
Tom
69
Numer
2
Strony
175-196
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-02-20
Twórcy
autor
  • Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
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  • [C] C. Carathéodory, Über eine spezielle Metrik die in der Theorie der analytischen Funktionen auftritt, Atti Pontifica Acad. Sci. Nuovi Lincei 80 (1927), 135-141.
  • [E] A. Edigarian, On extremal mappings in complex ellipsoids, Ann. Polon. Math. 62 (1995), 83-96.
  • [Ge] G. Gentili, Regular complex geodesics in the domain Dₙ = {(z₁,...,zₙ) ∈ ℂⁿ: |z₁|+...+|zₙ| < 1}, in: Lecture Notes in Math. 1277, Springer, 1987, 35-45.
  • [Gi] B. Gilligan, On the Kobayashi pseudometric reduction of homogeneous spaces, Canad. Math. Bull. 31 (1988), 45-51.
  • [HW] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Sci. Publ., 1978.
  • [HD] V. Z. Hristov and T. Davidov, Examples of typical Carathéodory and Kobayashi pseudodistances, C. R. Acad. Bulgare Sci. 39 (1986), 23-25.
  • [JP1] M. Jarnicki and P. Pflug, Some remarks on the product property, in: Proc. Sympos. Pure Math. 52 (Part 2), Amer. Math. Soc., 1991, 263-272.
  • [JP2] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993.
  • [JPZ] M. Jarnicki, P. Pflug and R. Zeinstra, Geodesics for convex complex ellipsoids, Ann. Scuola Norm. Sup. Pisa 20 (1993), 535-543.
  • [Kl1] M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances, Bull. Soc. Math. France 113 (1985), 231-240.
  • [Kl2] M. Klimek, Pluripotential Theory, Oxford Univ. Press, 1991.
  • [Ko1] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Pure and Appl. Math. 2, M. Dekker, 1970.
  • [Ko2] S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc. 82 (1976), 357-416.
  • [L1] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 327-479.
  • [L2] L. Lempert, Intrinsic distances and holomorphic retracts, Complex Analysis and Applications (Varna, 1981), Publ. House Bulgar. Acad. Sci., Sophia, 1984, 341-364.
  • [N] S. Nivoche, Pluricomplex Green function, capacitative notions and approximation problems in ℂⁿ, Indiana Univ. Math. J. 44 (1995), 489-510.
  • [Pa] M.-Y. Pang, Smoothness of the Kobayashi metric of non-convex domains, Internat. J. Math. 4 (1993), 953-987.
  • [PZ] P. Pflug and W. Zwonek, The Kobayashi metric for non-convex complex ellipsoids, Complex Variables 29 (1996), 59-71.
  • [R] H.-J. Reiffen, Die Carathéodory Distanz und ihre zugehörige Differentialmetrik, Math. Ann. 161 (1965), 315-324.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z2p175bwm
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