Comptes Rendus
no. 3-4
Complex Analysis
A remark on the Bergman kernels of the Cartan–Hartogs domains
[Une remarque sur le noyau de Bergman des domaines de Cartan–Hartogs]

Présenté par : Jean-Pierre Demailly

Atsushi Yamamori1
1 Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 157-160.

Nous obtenons une nouvelle formule pour le noyau de Bergman des domaines de Cartan–Hartogs. Comme application, nous étudions le problème du Lu QiKeng pour les domaines de Cartan–Hartogs.

We give a new formula for the Bergman kernels of the Cartan–Hartogs domains. As an application of our formula, we study the Lu Qi-Keng problem of the Cartan–Hartogs domains.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.01.005
Atsushi Yamamori 1

1 Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan 
@article{CRMATH_2012__350_3-4_157_0,
     author = {Atsushi Yamamori},
     title = {A remark on the {Bergman} kernels of the {Cartan{\textendash}Hartogs} domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {157--160},
     publisher = {Elsevier},
     volume = {350},
     number = {3-4},
     year = {2012},
     doi = {10.1016/j.crma.2012.01.005},
     language = {en},
}
TY  - JOUR
AU  - Atsushi Yamamori
TI  - A remark on the Bergman kernels of the Cartan–Hartogs domains
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 157
EP  - 160
VL  - 350
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2012.01.005
LA  - en
ID  - CRMATH_2012__350_3-4_157_0
ER  - 
%0 Journal Article
%A Atsushi Yamamori
%T A remark on the Bergman kernels of the Cartan–Hartogs domains
%J Comptes Rendus. Mathématique
%D 2012
%P 157-160
%V 350
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2012.01.005
%G en
%F CRMATH_2012__350_3-4_157_0
Atsushi Yamamori. A remark on the Bergman kernels of the Cartan–Hartogs domains. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 157-160. doi : 10.1016/j.crma.2012.01.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.005/

[1] H.P. Boas Lu Qi-Kengʼs problem, J. Korean Math. Soc., Volume 37 (2000), pp. 253-267

[2] D. Cvijovic Polypseudologarithms revisited, Phys. A, Volume 389 (2010), pp. 1594-1600

[3] F.Z. Demmad-Abdessameud Polynôme de Hua, noyau de Bergman des domaines de Cartan–Hartogs et problème de Lu Qikeng, Rend. Semin. Mat. Univ. Politec. Torino, Volume 67 (2009) no. 1, pp. 55-89

[4] E. Ligocka Forelli–Rudin constructions and weighted Bergman projections, Studia Math., Volume 94 (1989), pp. 257-272

[5] G. Roos Weighted Bergman kernels and virtual Bergman kernels, Sci. China Ser. A, Volume 48 (2005) no. suppl., pp. 225-237

[6] W. Yin The Bergman kernels on Cartan–Hartogs domains, Chinese Sci. Bull., Volume 44 (1999) no. 21, pp. 1947-1951

[7] A. Yamamori, The Bergman kernel of the Fock–Bargmann–Hartogs domain and the polylogarithm function, Complex Var. Elliptic Equ., , in press. | DOI

[8] A. Yamamori, An explicit computation of the Bergman kernel of a certain class of the Hartogs domains, preprint.

[9] L. Zhang; W. Yin Lu Qi-Kengʼs problem on some complex ellipsoids, J. Math. Anal. Appl., Volume 357 (2009) no. 2, pp. 364-370

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A note on the Bergman kernel of a certain Hartogs domain

Atsushi Yamamori

C. R. Math (2012)

On the localization of the minimum integral related to the weighted Bergman kernel and its application

Hyeseon Kim

C. R. Math (2017)