The Bergman kernel of the minimal ball and applications
Annales de l'Institut Fourier, Tome 47 (1997) no. 3, pp. 915-928.

Dans cette note on calcule le noyau de Bergman de la boule unité associé à la plus petite norme sur n qui prolonge la norme euclidienne sur n et nous donnons quelques applications.

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

@article{AIF_1997__47_3_915_0,
     author = {Oeljeklaus, Karl and Pflug, Peter and Youssfi, El Hassan},
     title = {The {Bergman} kernel of the minimal ball and applications},
     journal = {Annales de l'Institut Fourier},
     pages = {915--928},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {3},
     year = {1997},
     doi = {10.5802/aif.1585},
     mrnumber = {98d:32028},
     zbl = {0873.32025},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1585/}
}
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
SP  - 915
EP  - 928
VL  - 47
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1585/
DO  - 10.5802/aif.1585
LA  - en
ID  - AIF_1997__47_3_915_0
ER  - 
%0 Journal Article
%A Oeljeklaus, Karl
%A Pflug, Peter
%A Youssfi, El Hassan
%T The Bergman kernel of the minimal ball and applications
%J Annales de l'Institut Fourier
%D 1997
%P 915-928
%V 47
%N 3
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.1585/
%R 10.5802/aif.1585
%G en
%F AIF_1997__47_3_915_0
Oeljeklaus, Karl; Pflug, Peter; Youssfi, El Hassan. The Bergman kernel of the minimal ball and applications. Annales de l'Institut Fourier, Tome 47 (1997) no. 3, pp. 915-928. doi : 10.5802/aif.1585. http://www.numdam.org/articles/10.5802/aif.1585/

[Bel] S. Bell, Proper holomorphic mappings between circular domains, Comment. Math. Helv., 57 (1982), 532-538. | MR | Zbl

[Ber] F. Berteloot, Attraction des disques analytiques et hölderienne d'applications holomorphes propres, Banach Center Publications, 31 (1995), 91-98. | MR | Zbl

[DF] K. Diederich and J.E. Fornaess, Pseudoconvex Domains : Bounded Strictly Plurisubharmonic Exhaustion Functions, Inventiones Math., 39 (1977), 129-141. | Zbl

[FH] W. Fulton & J. Harris, Representation theory, Graduate Texts in Math., Springer-Verlag, 1991. | MR | Zbl

[HP] K.T. Hahn & P. Pflug, On a minimal complex norm that extends the euclidean norm, Monatsh. Math., 105 (1988), 107-112. | MR | Zbl

[JP] M. Jarnicki & P. Pflug, Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. | MR | Zbl

[Ki] K.T. Kim, Automorphism groups of certain domains in Cn with singular boundary, Pacific J. Math., 151 (1991), 54-64. | MR | Zbl

[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. | MR | Zbl

[OY] K. Oeljeklaus & E.H. Youssfi, Proper holomorphic mappings and related automorphism groups, J. Geom. Anal., to appear. | Zbl

[Pi1] S. Pinchuk, Scaling method and holomorphic mappings, Proc. Symposia in Pure Math., Part 1, 52 (1991). | MR | Zbl

[Pi2] S. Pinchuk, On proper holomorphic mappings on strictly pseudoconvex domains, Sib. Math. J., 15 (1974). | Zbl

[Th] A. Thomas, Uniform extendability of the Bergman kernel, Illinois J. Math., 39 (1995), 598-605. | MR | Zbl

Cité par Sources :