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

Yamamori, Atsushi1
1 Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Comptes Rendus. Mathématique, Tome 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
Yamamori, Atsushi 1

1 Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan 
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Yamamori, Atsushi. A remark on the Bergman kernels of the Cartan–Hartogs domains. Comptes Rendus. Mathématique, Tome 350 (2012) no. 3-4, pp. 157-160. doi : 10.1016/j.crma.2012.01.005. http://www.numdam.org/articles/10.1016/j.crma.2012.01.005/

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

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

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

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

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

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