Pacific Journal of Mathematics

A compact set that is locally holomorphically convex but not holomorphically convex.

Michael Freeman and Reese Harvey

Article information

Pacific J. Math., Volume 48, Number 1 (1973), 77-81.

First available in Project Euclid: 13 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation
Secondary: 32E20: Polynomial convexity


Freeman, Michael; Harvey, Reese. A compact set that is locally holomorphically convex but not holomorphically convex. Pacific J. Math. 48 (1973), no. 1, 77--81.

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  • [1] M. Freeman, Exceptional points of real submanifolds, (in preparation).
  • [2] T. Gamelin, Uniform Algebras, Prentice Hall, (1969).
  • [3] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., (2) 68 (1958), 460-472.
  • [4] R. Harvey, The theory of hyper functionson totally real subsets of a complex manifold with applications to extension problems, Amer. J. Math., 91 (1969), 853-873.
  • [5] R. Harvey and R. 0. Wells, Compact holomorphically convex subsets of a Stein manifold, Trans. Amer. Math. Soc, 136 (1969), 509-516.
  • [6] R. Harvey and R. 0. Wells, Holomorphic approximationon totally real submanifoldsof a complex manifold, Math. Ann., (to appear).
  • [7] R. Harvey and R. 0. Wells, Zero sets of nonnegative strictly plurisubharmonic functions,Math. Ann.. (to appear).
  • [8] L. Hormander, An Introduction to Complex Analysis in Several Variables, D. Van Nostrand, Princeton, N. J., (1966).
  • [9] L. Hormander and J. Wermer,Uniformapproximationon compact sets in Cn Math. Scand., 23 (1968), 5-21.
  • [10] S. N. Mergelyan, Uniform approximationto functionsof a complex variable, Amer. Math. Soc. Translation, 101 (1954).
  • [11] R. Nirenberg and R. 0. Wells, Approximationtheorems on differentiatesubman- ifolds of a complex manifold, Trans. Amer. Math. Soc, 142 (1969), 15-35.
  • [12] M. Sato, Theory of hyper functionsII, J. Fac. Sci. Univ. Tokyo, Sect. I, 8 (1960), 387-437.
  • [13] V. Vladimirov, Methods of the Theory of Functions of Several Complex Variables, The M. I. T. Press, Cambridge, Mass., (1966).