Browse > Article
http://dx.doi.org/10.4134/JKMS.2012.49.1.069

EXPLICIT FORMULAS FOR THE BERGMAN KERNEL ON CERTAIN FORELLI-RUDIN CONSTRUCTION  

Zhang, Liyou (School of Mathematical Science Capital Normal University)
Wang, An (School of Mathematical Science Capital Normal University)
Li, Qingbin (Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industry Management)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.1, 2012 , pp. 69-83 More about this Journal
Abstract
In this note, we present certain circular domain, named Forelli-Rudin construction or Hua construction, which is built on Cartan domains. We compute the explicit Bergman kernel for it and get the corresponding weighted Bergman kernel on its base.
Keywords
Bergman kernel; weighted Bergman kernel; Forelli-Rudin construction; Hua construction;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 A. Edigarian and W. Zwonek, Geometry of the symmetrized polydisc, Arch. Math. (Basel) 84 (2005), no. 4, 364-374.   DOI
2 M. Englis, A Forelli-Rudin construction and asymptotics of weighted Bergman kernels, J. Funct. Anal. 177 (2000), no. 2, 257-281.   DOI   ScienceOn
3 M. Englis and G. K. Zhang, On a generalized Forelli-Rudin construction, Complex Var. Elliptic Equ. 51 (2006), no. 3, 277-294.   DOI
4 F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602.   DOI
5 G. Francsics and N. Hanges, The Bergman kernel and hypergeometric functions, J. Funct. Anal. 142 (1996), no. 2, 494-510.   DOI   ScienceOn
6 L. G. Hua, Harmonic Analysis of Function of several Complex Variables in Classical Domains, Beijing, Science Press, 1959.
7 E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), no. 3, 257-272.   DOI
8 Q. K. Lu, The Classical Manifolds and Classical Domains, Shanghai: Shanghai Scientific and Technical Publisher, 1963.
9 S. Bergman, Uber die Entwickling der harmonischen Funktionen der Ebene und Raumes nach Orthogonal funktionen, Math. Ann. 96 (1922), 237.
10 S. Bergman, Uber die kernfunktion eines Bereiches und ihre Verhalten am Rande, J. Reine Angew. Math. 169 (1933), 1
11 S. Bergman, Uber die kernfunktion eines Bereiches und ihre Verhalten am Rande, J. Reine Angew. Math. 172 (1935), 89.
12 S. Bergman, Zur theorie Von pseudokonformen abbildungen, Mat. sb (N.S) 1 (1963), no. 1, 79-96.
13 A. Wang, W. P. Yin, L. Y. Zhang, and G. Roos, The Kahler-Einstein metric for some Hartogs domains over bounded symmetric domains, Sci. China Ser. A 49 (2006), no. 9, 1175-1210.   DOI   ScienceOn
14 K. Oeljeklaus, P. P ug, and E.H. Youssfi, The Bergman kernel of the minimal ball and applications, Ann. Inst. Fourier (Grenoble) 47 (1997), no. 3, 915-928.   DOI   ScienceOn
15 J. D. Park, New formulas of the Bergman kernel for complex ellipsoids in $C^2$, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4211-4221.   DOI   ScienceOn
16 G. Roos, Weighted Bergman kernels and virtual Bergman kernels, Sci. China Ser. A 48 (2005), suppl., 387-399.
17 H. P. Boas, Lu Qi-Keng's problem, J. Korean Math. Soc. 37 (2000), no. 2, 253-267.   과학기술학회마을
18 W. P. Yin, The Bergman Kernels on Cartan-Hartogs domains, Chinese Sci. Bull. 44 (1999), no. 21, 1947-1951.   DOI
19 W. P. Yin, The Bergman kernels on super-Cartan domains of the first type, Sci. China Ser. A 43 (2000), no. 1, 13-21.   DOI   ScienceOn
20 L. Y. Zhang and W. P. Yin, Lu Qi-Kengs problem on some complex ellipsoids, J. Math. Anal. Appl. 357 (2009), no. 2, 364-370.   DOI   ScienceOn
21 H. P. Boas, S. Q. Fu, and E. J. Straube, The Bergman kernel function: Explicit formulas and zeroes, Proc. Amer. Math. Soc. 127 (1999), no. 3, 805-811.   DOI   ScienceOn
22 J. P. D'Angelo, A note on the Bergman kernel, Duke Math. J. 45 (1978), no. 2, 259-265.   DOI
23 J. P. D'Angelo, An explicit computation of the Bergman kernel function, J. Geom. Anal. 4 (1994), no. 1, 23-34.   DOI