Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.1.285

ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL FOR TUBE DOMAIN OF INFINITE TYPE  

Lee, Hanjin (Global Leadership School Handong Global University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 285-303 More about this Journal
Abstract
The asymptotic expansions of the Bergman kernels on the diagonals near the boundary points of exponentially-flat infinite type for pseudoconvex tube domain in $\mathbb{C}^2$ are obtained.
Keywords
Bergman kernel; infinite type; tube domains;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. Bharali, On the growth of the Bergman kernel near an infinite-type point, Math. Ann. 347 (2010), no. 1, 1-13.   DOI
2 H. P. Boas, E. J. Straube, and J. Yu, Boundary limits of the Bergman kernel and metric, Michigan Math. J. 42 (1995), no. 3, 449-461.   DOI
3 D. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math Z. 200 (1989), no. 3, 429-466.   DOI
4 S. Cho, Boundary behavior of the Bergman kernel function on some pseudoconvex domains in ${\mathbb{C}^n}$, Trans. Amer. Math. Soc. 345 (1994), no. 2, 803-817.
5 K. Diederich, Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), 9-36.   DOI
6 K. Diederich, G. Herbort, and T. Ohsawa, The Bergman kernel on uniformly extendable pseudoconvex domains, Math. Ann. 273 (1986), no. 3, 471-478.   DOI
7 C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65.   DOI
8 L. Hormander, $L^2$ estimates and existence theorems for the $\bar{\partial}$ operator, Acta Math. 113 (1965), 89-152.   DOI
9 J. Kamimoto, Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in ${\mathbb{C}^2}$, Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 51-85.   DOI
10 J. Kamimoto, Newton polyhedra and the Bergman kernel, Math. Z. 246 (2004), no. 3, 405-440.   DOI
11 J. Kamimoto, The Bergman kernel on tube domain of finite type, J. Math. Sci. Univ. Tokyo 13 (2006), no. 3, 365-408.
12 K. Kim and S. Lee, Asymptotic behavior of the Bergman kernel and associated invariants in certain infinite type pseudoconvex domains, Forum Math. 14 (2002), no. 5, 775-795.
13 A. Koranyi, The Bergman kernel function for tubes over convex cones, Pacific J. Math. 12 (1962), no. 1, 1355-1359.   DOI
14 J. McNeal, Estimates on the Bergman kernels of convex domains, Adv. Math. 109 (1994), 108-139.   DOI   ScienceOn
15 E. V. Vinberg, The theory of homogeneous convex cones, Trudy Moskov. Math. Obsc. 12 (1963), 303-358; Trans. Moscow Math. Soc. 12 (1963), 303-358.