A remark on the Bergman kernels of the Cartan–Hartogs domains

Atsushi Yamamori

doi:10.1016/j.crma.2012.01.005

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 Yamamori ¹

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.

Abstract (VO)
Résumé

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.

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.

Reçu le : 2011-09-20
Accepté le : 2012-01-09
Publié le : 2012-01-20

DOI : 10.1016/j.crma.2012.01.005

Affiliations des auteurs :

Atsushi Yamamori ¹

¹ Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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     title = {A remark on the {Bergman} kernels of the {Cartan{\textendash}Hartogs} domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {157--160},
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     doi = {10.1016/j.crma.2012.01.005},
     language = {en},
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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/

Bibliographie
Cité par

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[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

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[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

Hideyuki Ishi; Jong-Do Park; Atsushi Yamamori Bergman Kernel Function for Hartogs Domains Over Bounded Homogeneous Domains, The Journal of Geometric Analysis, Volume 27 (2017) no. 2, p. 1703 | DOI:10.1007/s12220-016-9737-4
Yihong Hao; An Wang The Bergman kernels of generalized Bergman–Hartogs domains, Journal of Mathematical Analysis and Applications, Volume 429 (2015) no. 1, p. 326 | DOI:10.1016/j.jmaa.2015.04.023
Atsushi Yamamori Automorphisms of normal quasi-circular domains, Bulletin des Sciences Mathématiques, Volume 138 (2014) no. 3, p. 406 | DOI:10.1016/j.bulsci.2013.10.002

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