Pacific Journal of Mathematics

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

Michael Freeman and Reese Harvey

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Article information

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

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102945702

Mathematical Reviews number (MathSciNet)
MR0326004

Zentralblatt MATH identifier
0277.32009

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

Citation

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. https://projecteuclid.org/euclid.pjm/1102945702


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References

  • [1] M. Freeman, Exceptional points of real submanifolds, (in preparation).
  • [2] T. Gamelin, Uniform Algebras, Prentice Hall, (1969).
    Mathematical Reviews (MathSciNet): MR53:14137
  • [3] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math., (2) 68 (1958), 460-472.
    Mathematical Reviews (MathSciNet): MR20:5299
    Zentralblatt MATH: 0108.07804
  • [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.
    Mathematical Reviews (MathSciNet): MR41:2051
    Zentralblatt MATH: 0202.36602
  • [5] R. Harvey and R. 0. Wells, Compact holomorphically convex subsets of a Stein manifold, Trans. Amer. Math. Soc, 136 (1969), 509-516.
    Mathematical Reviews (MathSciNet): MR38:3470
    Zentralblatt MATH: 0175.37204
  • [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).
    Mathematical Reviews (MathSciNet): MR34:2933
    Zentralblatt MATH: 0138.06203
  • [9] L. Hormander and J. Wermer,Uniformapproximationon compact sets in Cn Math. Scand., 23 (1968), 5-21.
    Mathematical Reviews (MathSciNet): MR40:7484
    Zentralblatt MATH: 0181.36201
  • [10] S. N. Mergelyan, Uniform approximationto functionsof a complex variable, Amer. Math. Soc. Translation, 101 (1954).
    Mathematical Reviews (MathSciNet): MR15:612h
    Zentralblatt MATH: 0059.05902
  • [11] R. Nirenberg and R. 0. Wells, Approximationtheorems on differentiatesubman- ifolds of a complex manifold, Trans. Amer. Math. Soc, 142 (1969), 15-35.
    Mathematical Reviews (MathSciNet): MR39:7140
    Zentralblatt MATH: 0188.39103
  • [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).
    Mathematical Reviews (MathSciNet): MR34:1551

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