Oeljeklaus, Karl; Pflug, Peter; Youssfi, El Hassan The Bergman kernel of the minimal ball and applications. (English) Zbl 0873.32025 Ann. Inst. Fourier 47, No. 3, 915-928 (1997). Summary: In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in \(\mathbb{C}^{n}\) that extends the euclidean norm in \(\mathbb{R}^{n}\), and give some applications. Cited in 2 ReviewsCited in 26 Documents MSC: 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32H35 Proper holomorphic mappings, finiteness theorems Keywords:Bergman kernel; minimal ball; proper holomorphic mapping × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [Bel] , Proper holomorphic mappings between circular domains, Comment. Math. Helv., 57 (1982), 532-538. · Zbl 0511.32013 [2] [Ber] , Attraction des disques analytiques et hölderienne d’applications holomorphes propres, Banach Center Publications, 31 (1995), 91-98. · Zbl 0831.32012 [3] [DF] and , Pseudoconvex Domains : Bounded Strictly Plurisubharmonic Exhaustion Functions, Inventiones Math., 39 (1977), 129-141. · Zbl 0353.32025 [4] [FH] & , Representation theory, Graduate Texts in Math., Springer-Verlag, 1991. · Zbl 0744.22001 [5] [HP] & , On a minimal complex norm that extends the euclidean norm, Monatsh. Math., 105 (1988), 107-112. · Zbl 0638.32005 [6] [JP] & , Invariant Distances and Metrics in Complex Analysis, Walter de Gruyter, 1993. · Zbl 0789.32001 [7] [Ki] , Automorphism groups of certain domains in Cn with singular boundary, Pacific J. Math., 151 (1991), 54-64. · Zbl 0698.32016 [8] [Le] , Les noyaux de Bergman et Szegö pour des domaines strictement pseudo-convexes généralisent la boule, Publicationes Math., 36 (1992), 65-72. · Zbl 0765.32014 [9] [OY] & , Proper holomorphic mappings and related automorphism groups, J. Geom. Anal., to appear. · Zbl 0942.32019 [10] [Pi1] , Scaling method and holomorphic mappings, Proc. Symposia in Pure Math., Part 1, 52 (1991). · Zbl 0744.32013 [11] [Pi2] , On proper holomorphic mappings on strictly pseudoconvex domains, Sib. Math. J., 15 (1974). · Zbl 0303.32016 [12] [Th] , Uniform extendability of the Bergman kernel, Illinois J. Math., 39 (1995), 598-605. · Zbl 0849.32016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.