Integral representations and the complex Monge-Ampère equation in strictly convex domains
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- by Nancy K. Stanton PDF
- Proc. Amer. Math. Soc. 75 (1979), 276-278 Request permission
Abstract:
We prove a relationship between Aǐzenberg’s integral representation formula for holomorphic functions in a strictly convex domain and the complex Monge-Ampère equation.References
- Patrick Ahern and Robert Schneider, The boundary behavior of Henkin’s kernel, Pacific J. Math. 66 (1976), no. 1, 9–14. MR 435449 L. A. Aǐzenberg, Integral representations of functions which are holomorphic in convex regions of ${{\mathbf {C}}^n}$ space, Dokl. Akad. Nauk SSSR 151 (1963), 1247-1249; English, transl., Soviet Math. Dokl. 4 (1963), 1149-1152.
- Charles L. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. (2) 103 (1976), no. 2, 395–416. MR 407320, DOI 10.2307/1970945
- François Norguet, Introduction aux fonctions de plusieurs variables complexes: représentations intégrales, Fonctions de plusieurs variables complexes (Sém. François Norguet, 1970–1973; à la mémoire d’André Martineau), Lecture Notes in Math., Vol. 409, Springer, Berlin, 1974, pp. 1–97 (French). MR 0369729
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 276-278
- MSC: Primary 32A25
- DOI: https://doi.org/10.1090/S0002-9939-1979-0532150-2
- MathSciNet review: 532150