The Bergman kernel of the minimal ball and applications

Karl Oeljeklaus; Peter Pflug; El Hassan Youssfi

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 3, page 915-928
  • ISSN: 0373-0956

Abstract

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In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in ℂ n that extends the euclidean norm in ℝ n and give some applications.

How to cite

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Oeljeklaus, Karl, Pflug, Peter, and Youssfi, El Hassan. "The Bergman kernel of the minimal ball and applications." Annales de l'institut Fourier 47.3 (1997): 915-928. <http://eudml.org/doc/75249>.

@article{Oeljeklaus1997,
abstract = {In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in $\{\Bbb C\}^\{n\}$ that extends the euclidean norm in $\{\Bbb R\}^\{n\}$ and give some applications.},
author = {Oeljeklaus, Karl, Pflug, Peter, Youssfi, El Hassan},
journal = {Annales de l'institut Fourier},
keywords = {Bergman kernel; minimal ball; proper holomorphic mapping},
language = {eng},
number = {3},
pages = {915-928},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Bergman kernel of the minimal ball and applications},
url = {http://eudml.org/doc/75249},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Oeljeklaus, Karl
AU - Pflug, Peter
AU - Youssfi, El Hassan
TI - The Bergman kernel of the minimal ball and applications
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 3
SP - 915
EP - 928
AB - In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in ${\Bbb C}^{n}$ that extends the euclidean norm in ${\Bbb R}^{n}$ and give some applications.
LA - eng
KW - Bergman kernel; minimal ball; proper holomorphic mapping
UR - http://eudml.org/doc/75249
ER -

References

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  2. [Ber] F. BERTELOOT, Attraction des disques analytiques et hölderienne d'applications holomorphes propres, Banach Center Publications, 31 (1995), 91-98. Zbl0831.32012MR96k:32054
  3. [DF] K. DIEDERICH and J.E. FORNAESS, Pseudoconvex Domains : Bounded Strictly Plurisubharmonic Exhaustion Functions, Inventiones Math., 39 (1977), 129-141. Zbl0353.32025
  4. [FH] W. FULTON & J. HARRIS, Representation theory, Graduate Texts in Math., Springer-Verlag, 1991. Zbl0744.22001MR93a:20069
  5. [HP] K.T. HAHN & P. PFLUG, On a minimal complex norm that extends the euclidean norm, Monatsh. Math., 105 (1988), 107-112. Zbl0638.32005MR89a:32031
  6. [JP] M. JARNICKI & P. PFLUG, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. Zbl0789.32001MR94k:32039
  7. [Ki] K.T. KIM, Automorphism groups of certain domains in Cn with singular boundary, Pacific J. Math., 151 (1991), 54-64. Zbl0698.32016MR92j:32117
  8. [Le] J.J. LOEB, Les noyaux de Bergman et Szegö pour des domaines strictement pseudo-convexes généralisent la boule, Publicationes Math., 36 (1992), 65-72. Zbl0765.32014MR93g:32034
  9. [OY] K. OELJEKLAUS & E.H. YOUSSFI, Proper holomorphic mappings and related automorphism groups, J. Geom. Anal., to appear. Zbl0942.32019
  10. [Pi1] S. PINCHUK, Scaling method and holomorphic mappings, Proc. Symposia in Pure Math., Part 1, 52 (1991). Zbl0744.32013MR92i:32031
  11. [Pi2] S. PINCHUK, On proper holomorphic mappings on strictly pseudoconvex domains, Sib. Math. J., 15 (1974). Zbl0303.32016
  12. [Th] A. THOMAS, Uniform extendability of the Bergman kernel, Illinois J. Math., 39 (1995), 598-605. Zbl0849.32016MR96i:32025

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