This is a preview of subscription content, log in via an institution to check access.
References
Berndtsson, B., Anderson, M.: Henkin-Ramirez formulas with weight factors. Ann. Inst. Fourier (Grenoble)32, 91–110 (1983)
Berndtsson, B.: Integral kernels and approximation on totally real submanifolds of ℂn. Math. Ann.243, 125–129 (1979)
Bruna, J.: Núcleos de Cauchy en dominios estrictamente pseudoconvexos y operadores integrales que invierten la ecuación\(\bar \partial \), to appear in a collection of papers edited in occassion of the retirement of Prof. J. L. Vigil by the “Departamento de Teoria de Funciones”, Facultad de Ciencias, Zaragoza, Spain
Chollet, A.M.: Ensembles des zéros a la frontière des fonctions analytiques dans les domaines strictement pseudoconvexes. Ann. Inst. Fourier (Grenoble)26, 51–80 (1976)
Čirka, E.M.: Approximation by holomorphic functions on smooth submanifolds in ℂn Mat. Sborn.78, 120 (1969); A.M.S. Transl.: Math. USSR Sborn.7, 95–114 (1969)
O'Farrell, A.G., Preskenis, K.J.: Approximation by polynomials in two complex variables. Math. Ann.246, 225–232 (1980)
O'Farrell, A.G., Preskenis, K.J., Walsh, D.: Polynomial approximation on graphs. Math. Ann.266, 73–81 (1983)
O'Farrell, A.G., Preskenis, K.J., Walsh, D.: Holomorphic approximation in Lipschitz norms. Maynooth Mathematics preprint series, 1983–4, Co. Kildare, Ireland
Harvey, F.R., Wells, R.O.: Holomorphic approximation and hyperfunction theory on aC 1 totally real submanifold of a complex manifold. Math. Ann.197, 287–318 (1972)
Harvey, F.R., Wells, R.O.: Zero sets of non-negative strictly plurisubharmonic functions. Math. Ann.201, 165–170 (1973)
Henkin, G.M., Leiterer, J.: Theory of functions on strictly pseudo convex sets with nonsmooth boundary. Akademie der Wissenschaften der DDR Institut für Mathematik, Berlin, 1981
Hörmander, L., Wermer, J.: Uniform approximation on compact subsets in ℂn. Math. Scand.23, 5–21 (1968)
Malgrange, B.: Ideals of differentiable functions. Bombay: Tata Institute 1966
Nirenberg, R., Wells, R.O.: Approximation theorems on differentiable submanifolds of a complex manifold. Trans. Am. Math. Soc.142, 15–35 (1969)
Nunemacher, J.: Approximation theory on totally real submanifolds. Math. Ann.224, 129–141 (1976)
Range, R.M., Siu, Y.T.:C k approximation by holomorphic functions and\(\bar \partial \)-closed forms onC k submanifolds of a complex manifold. Math. Ann.210, 105–122 (1974)
Rudin, W.: Real and complex analysis. New York: McGraw-Hill 1974
Sakai, A.: Uniform approximation in several complex variables. Osaka J. Math.15, 589–611 (1978)
Sakai, A.: Uniform approximation on totally real sets. Math. Ann.253, 139–144 (1980)
Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970
Weinstock, B.: A new proof of a theorem of Hörmander and Wermer. Math. Ann.200, 59–64 (1976)
Weinstock, B.: Uniform approximation on the graph of a smooth map in ℂn. Can. J. Math.32, 1390–1396 (1980)
Author information
Authors and Affiliations
Additional information
This work has been partially supported by a grant of the “Comisión Asesora de Investigación Cientifica y Técnica”, Ministerio de Educación y Ciencia, Madrid
Rights and permissions
About this article
Cite this article
Bruna, J., Burgués, J.M. Holomorphic approximation inC m-norms on totally real compact sets in ℂn . Math. Ann. 269, 103–117 (1984). https://doi.org/10.1007/BF01455999
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01455999