References
Alexander, H. &Taylor, B. A., Comparison of two capacities in Cn.Math. Z., 186 (1984), 407–417.
Aytuna, A., Algebraicity of certain complex analytic subsets of CN: a functional analysis point of view.Linear Topol. Spaces Complex Anal., 1 (1994), 1–13.
Bedford, E., The operator(dd c)n on complex spaces, inSeminar Pierre Lelong-Henry Skoda (Analysis), 1980/1981, pp. 293–324. Lecture Notes in Math., 919. Springer-Verlag, Berlin-New York, 1982.
Bernstein, S. N., Sur l'ordre de la meilleure approximation des fonctions continues par des poynomes de degré donne.Acad. Roy. Belgique Cl. Sci. Mém. Coll. in 4 0 (Sér. 2), 4:1 (1912), 1–104.
Bos, L., Levenberg, N., Milman, P. &Taylor, B. A., Tangential Markov inequalities characterize algebraic submanifolds of RN.Indiana Univ. Math. J., 44 (1995), 115–138.
Bedford, E. &Taylor, B. A., A new capacity for plurisubharmonic functions.Acta Math., 149 (1982), 1–40.
— Plurisubharmonic functions with logarithmic singularities.Ann. Inst. Fourier (Grenoble), 38:4 (1988), 133–171.
Chirka, E. M.,Complex Analytic Sets. Math. Appl. (Soviet Ser.), 46. Kluwer, Dordrecht, 1989.
Demailly, J. P., Mesures de Monge-Ampère et caractérisation des variétés algébriques affines.Mém. Soc. Math. France (N.S.), 19 (1985), 1–25.
—, Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité.Acta Math., 159 (1987), 153–169.
Fefferman, C. &Narasimhan, R., Bernstein's inequality on algebraic curves.Ann. Inst. Fourier (Grenoble), 43 (1993), 1319–1348.
—, A local Bernstein inequality on real algebraic varieties.Math. Z., 233 (1996), 673–692.
Fornæss, J. E. &Narasimhan, R., The Levi problem on complex spaces with singularities.Math. Ann., 248 (1980), 47–72.
Harris, J.,Algebraic Geometry, Graduate Texts in Math., 133, Springer-Verlag, New York, 1992.
Hörmander, L.,An Introduction to Complex Analysis in Several Variables, 3rd edition. North-Holland Math. Library, 7, North-Holland, Amsterdam-New York, 1990.
[Ho2]—,Notions of Converity. Progr. Math., 127. Birkhäuser Boston, Boston, MA, 1994.
Kiselman, C. O., Densité des fonctions plurisousharmoniques.Bull. Soc. Math. France, 107 (1979), 295–304.
—, Attenuating the singularities of plurisubharmonic functions.Ann. Polon. Math., 60 (1994) 173–197.
Klimek, M.,Pluripotential Theory. London Math. Soc. Monographs (N. S.), 6. Oxford Univ. Press, New York, 1991.
Leja, F., Sur les suites de polynômes, les ensembles fermés et la fonction de Green.Ann. Soc. Polon. Math., 12 (1934), 57–71.
Lelong, P.,Fonctions plurisousharmoniques et formes différentielles positives. Gordon & Breach. Paris-London-New York (distributed by Dunod éditeur, Paris), 1968.
— Thèorème de Banach-Steinhaus pour les polynomes; applications entières d'espaces vectoriels topologiques, inSéminaire Pierre Lelong (Analyse), 1970, pp. 87–112. Lecture Notes in Math., 205. Springer-Verlag, Berlin, 1971.
Lelong, P. &Gruman, L.,Entire Functions of Several Complex Variables. Grundlehren Math. Wiss., 282. Springer-Verlag, Berlin-New York, 1986.
Plesniak, W., Remarques sur une généralisation de l'inégalité de S. Bernstein.C. R. Acad. Sci. Paris Sér. I Math., 284 (1977), 1211–1213.
Ragozin, D. L., Polynomial approximation on compact manifolds and homogenous spaces.Trans. Amer. Math. Soc., 150 (1970), 41–53.
Ransford, T.,Potential Theory in the Complex Plane. London Math. Soc. Stud. Texts, 28. Cambridge Univ. Press, Cambridge, 1995.
Rudin, W., A geometric criterion for algebraic varieties.J. Math. Mech., 17 (1967/68), 671–683.
Sadullaev, A., A criterion for the algebraicity of analytic sets, inOn Holomorphic Functions of Several Complex Variables, pp. 107–122. Akad. Nauk. SSSR Sibirsk. Otdel., Inst. Fiz., Krasnoyarsk, 1976 (Russian).
—, An estimate for polynomials on analytic sets.Math. USSR-Izv., 20:3 (1983), 493–502.
—, Plurisubharmonic measures and capacities on complex manifolds.Russian Math. Surveys, 36:4 (1981) 53–105.
Siciak, J., On some extremal functions and their applications in the theory of analytic functions in several variables.Trans. Amer. Math. Soc., 105 (1962), 322–357.
— Extremal plurisubharmonic functions in CN Ann. Polon. Math., 39 (1981), 175–211.
Siciak, J.,Extremal plurisubharmonic functions and capacities in C n. Sophia Kokyuroku in Math., 14. Tokyo, 1982.
Singer, I.,Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Grundlehren Math. Wiss., 171. Springer-Verlag, New York-Berlin, 1970.
Siu, Y. T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents.Invent. Math., 27 (1974), 53–156.
Stoll, W.,Value Distribution on Parabolic Spaces. Lecture Notes in Math., 600. Springer-Verlag, Berlin-New York, 1977.
— The growth of the area of a transcendental analytic set, I; II.Math. Ann., 156 (1964), 47–78; 144–170.
Walsh, J. L.,Interpolation and Approximation by Rational Functions in the Complex Domain, 3rd edition. Amer. Math. Soc. Colloq. Publ., 20. Amer. Math. Soc., Providence, RI, 1960.
Zahariuta, V. P., Extremal plurisubharmonic functions, Hilbert scales and the isomorphisms of spaces of analytic functions of several complex variables, I; II.Teor. Funktsiį Funktsional. Anal. i Prilozhen., 19 (1974), 133–157; 21 (1974), 65–83 (Russian).
— Extremal plurisubharmonic functions, orthogonal polynomials and Bernstein-Walsh theorem for analytic functions of several complex variables.Ann. Polon. Math., 33 (1976), 137–148 (Russian).
— Spaces of analytic functions and complex potential theory.Linear Topol. Spaces Complex Anal., 1 (1994), 74–146.
Zeriahi, A., Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines.Ann. Inst. Fourier (Grenoble), 37:2 (1987), 79–104.
— Fonction de Green pluricomplexe à pôle à l'infini sur un espace de Stein parabolique.Math. Scand., 69 (1991), 89–126.
— Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique.Ann. Polon. Math., 63 (1996), 35–50.
— Pluricomplex Green functions and approximation of holomorphic functions, inComplex Analysis, Harmonic Analysis and Applications (Bordeaux, 1995), pp. 104–142. Pitman Res. Notes Math. Ser., 347. Longman, Harlow, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zeriahi, A. A criterion of algebraicity for Lelong classes and analytic sets. Acta Math. 184, 113–143 (2000). https://doi.org/10.1007/BF02392783
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02392783